 7.7.6.1: VOCABULARY Copy and complete: The sine ratio compares the length of...
 7.7.1.1: VOCABULARY Copy and complete: A set of three positive integers a, b...
 7.7.7.1: VOCABULARY Copy and complete: To solve a right triangle means to fi...
 7.7.2.1: VOCABULARY What is the longest side of a right triangle called?
 7.1: Copy and complete: A Pythagorean triple is a set of three positive ...
 7.7.3.1: VOCABULARY Copy and complete: Two triangles are ? if their correspo...
 7.7.4.1: VOCABULARY Copy and complete: A triangle with two congruent sides a...
 7.7.5.1: VOCABULARY Copy and complete: The tangent ratio compares the length...
 7.7.6.2: WRITING Explain how to tell which side of a right triangle is adjac...
 7.7.1.2: WRITING Describe the information you need to have in order to use t...
 7.7.7.2: WRITING Explain when to use a trigonometric ratio to find a side le...
 7.7.2.2: WRITING Explain how the side lengths of a triangle can be used to c...
 7.2: WRITING What does it mean to solve a right triangle? What do you ne...
 7.7.3.2: WRITING In your own words, explain geometric mean.
 7.7.4.2: WRITING Explain why the acute angles in an isosceles right triangle...
 7.7.5.2: WRITING Explain how you know that all right triangles with an acute...
 7.7.6.3: FINDING SINE RATIOS Find sin D and sin E. Write each answer as a fr...
 7.7.1.3: ALGEBRA Find the length of the hypotenuse of the right triangle. 1205
 7.7.7.3: USING INVERSE TANGENTS Use a calculator to approximate the measure ...
 7.7.2.3: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.3: WRITING Describe the difference between an angle of depression and ...
 7.7.3.3: IDENTIFYING SIMILAR TRIANGLES Identify the three similar right tria...
 7.7.4.3: 458458908 TRIANGLES Find the value of x. Write your answer in sim...
 7.7.5.3: FINDING TANGENT RATIOS Find tan A and tan B. Write each answer as a...
 7.7.6.4: FINDING SINE RATIOS Find sin D and sin E. Write each answer as a fr...
 7.7.1.4: ALGEBRA Find the length of the hypotenuse of the right triangle. x5633
 7.7.7.4: USING INVERSE TANGENTS Use a calculator to approximate the measure ...
 7.7.2.4: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.4: Find the unknown side length x. 6x
 7.7.3.4: IDENTIFYING SIMILAR TRIANGLES Identify the three similar right tria...
 7.7.4.4: 458458908 TRIANGLES Find the value of x. Write your answer in sim...
 7.7.5.4: FINDING TANGENT RATIOS Find tan A and tan B. Write each answer as a...
 7.7.6.5: FINDING SINE RATIOS Find sin D and sin E. Write each answer as a fr...
 7.7.1.5: ALGEBRA Find the length of the hypotenuse of the right triangle. 42 40
 7.7.7.5: USING INVERSE TANGENTS Use a calculator to approximate the measure ...
 7.7.2.5: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.5: Find the unknown side length x. 10x 6
 7.7.3.5: FINDING ALTITUDES Find the length of the altitude to the hypotenuse...
 7.7.4.5: 458458908 TRIANGLES Find the value of x. Write your answer in sim...
 7.7.5.5: FINDING TANGENT RATIOS Find tan A and tan B. Write each answer as a...
 7.7.6.6: ERROR ANALYSIS Explain why the students statement is incorrect. Wri...
 7.7.1.6: ERROR ANALYSIS Describe and correct the error in using the Pythagor...
 7.7.7.6: USING INVERSE SINES AND COSINES Use a calculator to approximate the...
 7.7.2.6: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.6: Find the unknown side length x. 12 x369
 7.7.3.6: FINDING ALTITUDES Find the length of the altitude to the hypotenuse...
 7.7.4.6: MULTIPLE CHOICE Find the length of }AC . A 7 }2 in. B 2 }7 in.C 7}}...
 7.7.5.6: FINDING LEG LENGTHS Find the value of x to the nearest tenth. 12418x
 7.7.6.7: FINDING COSINE RATIOS Find cos X and cos Y. Write each answer as a ...
 7.7.1.7: ERROR ANALYSIS Describe and correct the error in using the Pythagor...
 7.7.7.7: USING INVERSE SINES AND COSINES Use a calculator to approximate the...
 7.7.2.7: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.7: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.7: FINDING ALTITUDES Find the length of the altitude to the hypotenuse...
 7.7.4.7: ISOSCELES RIGHT TRIANGLE The square tile shown has painted corners ...
 7.7.5.7: FINDING LEG LENGTHS Find the value of x to the nearest tenth. 15278x
 7.7.6.8: FINDING COSINE RATIOS Find cos X and cos Y. Write each answer as a ...
 7.7.1.8: FINDING A LENGTH Find the unknown leg length x. 16.7 ftx8.9 ft
 7.7.7.8: USING INVERSE SINES AND COSINES Use a calculator to approximate the...
 7.7.2.8: VERIFYING RIGHT TRIANGLES Tell whether the triangle is a right tria...
 7.8: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.8: COMPLETING PROPORTIONS Write a similarity statement for the three s...
 7.7.4.8: 308608908 TRIANGLES Find the value of each variable. Write your a...
 7.7.5.8: FINDING LEG LENGTHS Find the value of x to the nearest tenth. 22588
 7.7.6.9: FINDING COSINE RATIOS Find cos X and cos Y. Write each answer as a ...
 7.7.1.9: FINDING A LENGTH Find the unknown leg length x. 9.8 in.13.4 in.x
 7.7.7.9: MULTIPLE CHOICE Which expression is correct? A sin 21 JL }JK 5 m J ...
 7.7.2.9: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.9: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.9: COMPLETING PROPORTIONS Write a similarity statement for the three s...
 7.7.4.9: 308608908 TRIANGLES Find the value of each variable. Write your a...
 7.7.5.9: FINDING LEG LENGTHS Find the value of x using the definition of tan...
 7.7.6.10: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.10: FINDING A LENGTH Find the unknown leg length x. 5.7 ft 4.9 ftx
 7.7.7.10: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.10: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.10: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.10: COMPLETING PROPORTIONS Write a similarity statement for the three s...
 7.7.4.10: 308608908 TRIANGLES Find the value of each variable. Write your a...
 7.7.5.10: FINDING LEG LENGTHS Find the value of x using the definition of tan...
 7.7.6.11: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.11: FINDING THE AREA Find the area of the isosceles triangle. 7 m 17 m16 m
 7.7.7.11: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.11: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.11: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.11: ERROR ANALYSIS Describe and correct the error in writing a proporti...
 7.7.4.11: SPECIAL RIGHT TRIANGLES Copy and complete the table. ab4584 a 7 ? ?...
 7.7.5.11: FINDING LEG LENGTHS Find the value of x using the definition of tan...
 7.7.6.12: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.12: FINDING THE AREA Find the area of the isosceles triangle. 20 ft 20 ...
 7.7.7.12: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.12: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.12: Classify the triangle formed by the side lengths as acute, right, o...
 7.7.3.12: ERROR ANALYSIS Describe and correct the error in writing a proporti...
 7.7.4.12: SPECIAL RIGHT TRIANGLES Copy and complete the table. ef d3086 d 5??...
 7.7.5.12: SPECIAL RIGHT TRIANGLES Find tan 308 and tan 458 using the 458458...
 7.7.6.13: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.13: FINDING THE AREA Find the area of the isosceles triangle. 10 cm 10 ...
 7.7.7.13: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.13: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.13: Find the value of x. 6 x9
 7.7.3.13: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.13: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.13: ERROR ANALYSIS Describe the error in the statement of the tangent r...
 7.7.6.14: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.14: FINDING SIDE LENGTHS Find the unknown side length of the right tria...
 7.7.7.14: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.14: VERIFYING RIGHT TRIANGLES Tell whether the given side lengths of a ...
 7.14: Find the value of x. x 94
 7.7.3.14: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.14: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.14: ERROR ANALYSIS Describe the error in the statement of the tangent r...
 7.7.6.15: USING SINE AND COSINE RATIOS Use a sine or cosine ratio to find the...
 7.7.1.15: FINDING SIDE LENGTHS Find the unknown side length of the right tria...
 7.7.7.15: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.15: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.15: Find the value of x. 64
 7.7.3.15: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.15: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.15: WRITING Describe what you must know about a triangle in order to us...
 7.7.6.16: SPECIAL RIGHT TRIANGLES Use the 458458908 Triangle Theorem to fin...
 7.7.1.16: FINDING SIDE LENGTHS Find the unknown side length of the right tria...
 7.7.7.16: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.16: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.16: Find the value of x. 52x
 7.7.3.16: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.16: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.16: MULTIPLE CHOICE Which expression can be used to find the value of x...
 7.7.6.17: WRITING Describe what you must know about a triangle in order to us...
 7.7.1.17: MULTIPLE CHOICE What is the length of the hypotenuse of a right tri...
 7.7.7.17: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.17: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.17: Find the value of x. 1216 x
 7.7.3.17: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.17: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.17: MULTIPLE CHOICE What is the approximate value of x in the triangle ...
 7.7.6.18: MULTIPLE CHOICE In nPQR, which expression can be used to find PQ? A...
 7.7.1.18: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.18: SOLVING RIGHT TRIANGLES Solve the right triangle. Round decimal ans...
 7.7.2.18: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.18: Find the value of x. 2025x
 7.7.3.18: FINDING LENGTHS Find the value of the variable. Round decimal answe...
 7.7.4.18: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.18: FINDING LEG LENGTHS Use a tangent ratio to find the value of x. Rou...
 7.7.6.19: ALGEBRA Find the value of x. Round decimals to the nearest tenth.
 7.7.1.19: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.19: ERROR ANALYSIS Describe and correct the students error in using an ...
 7.7.2.19: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.19: Find the value of x. Write your answer in simplest radical form. x66
 7.7.3.19: MULTIPLE CHOICE Use the diagram at the right. Decide which proporti...
 7.7.4.19: MULTIPLE CHOICE Which side lengths do not represent a 308608908 t...
 7.7.5.19: FINDING LEG LENGTHS Use a tangent ratio to find the value of x. Rou...
 7.7.6.20: ALGEBRA Find the value of x. Round decimals to the nearest tenth.
 7.7.1.20: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.20: ERROR ANALYSIS Describe and correct the students error in using an ...
 7.7.2.20: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.20: Find the value of x. Write your answer in simplest radical form. x 143
 7.7.3.20: MULTIPLE CHOICE In the diagram in Exercise 19 above, AC 5 36 and BC...
 7.7.4.20: ERROR ANALYSIS Describe and correct the error in finding the length...
 7.7.5.20: FINDING LEG LENGTHS Use a tangent ratio to find the value of x. Rou...
 7.7.6.21: ALGEBRA Find the value of x. Round decimals to the nearest tenth.
 7.7.1.21: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.21: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.21: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.21: Find the value of x. Write your answer in simplest radical form. 8 ...
 7.7.3.21: ALGEBRA Find the value(s) of the variable(s). a 1 5 1812
 7.7.4.21: ERROR ANALYSIS Describe and correct the error in finding the length...
 7.7.5.21: FINDING AREA Find the area of the triangle. Round to the nearest te...
 7.7.5.22: FINDING AREA Find the area of the triangle. Round to the nearest te...
 7.7.6.22: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.22: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.22: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.22: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.22: In Exercises 22 and 23, use the diagram. The angle between the bott...
 7.7.3.22: ALGEBRA Find the value(s) of the variable(s). 8 b 1 36
 7.7.4.22: WRITING Abigail solved Example 5 on page 459 in a different way. In...
 7.7.5.23: FINDING AREA Find the area of the triangle. Round to the nearest te...
 7.7.6.23: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.23: PYTHAGOREAN TRIPLES The given lengths are two sides of a right tria...
 7.7.7.23: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.23: CLASSIFYING TRIANGLES In Exercises 1523, decide if the segment leng...
 7.23: In Exercises 22 and 23, use the diagram. In Exercise 22, how tall i...
 7.7.3.23: ALGEBRA Find the value(s) of the variable(s). y 1612
 7.7.4.23: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.24: FINDING PERIMETER Find the perimeter of the triangle. Round to the ...
 7.7.6.24: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.24: FINDING SIDE LENGTHS Find the unknown side length x. Write your ans...
 7.7.7.24: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.24: MULTIPLE CHOICE Which side lengths do not form a right triangle? A ...
 7.24: Find the value of x to the nearest tenth. 548x3
 7.7.3.24: USING THEOREMS Tell whether the triangle is a right triangle. If so...
 7.7.4.24: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.25: FINDING PERIMETER Find the perimeter of the triangle. Round to the ...
 7.7.6.25: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.25: FINDING SIDE LENGTHS Find the unknown side length x. Write your ans...
 7.7.7.25: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.25: MULTIPLE CHOICE What type of triangle has side lengths of 4, 7, and...
 7.25: Find the value of x to the nearest tenth. 258x20
 7.7.3.25: USING THEOREMS Tell whether the triangle is a right triangle. If so...
 7.7.4.25: ALGEBRA Find the value of each variable. Write your answers in simp...
 7.7.5.26: FINDING PERIMETER Find the perimeter of the triangle. Round to the ...
 7.7.6.26: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.26: FINDING SIDE LENGTHS Find the unknown side length x. Write your ans...
 7.7.7.26: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.26: ERROR ANALYSIS A student tells you that if you double all the sides...
 7.26: Find the value of x to the nearest tenth. 38810x
 7.7.3.26: USING THEOREMS Tell whether the triangle is a right triangle. If so...
 7.7.4.26: CHALLENGE nABC is a 308608908 triangle. Find the coordinates of A...
 7.7.5.27: FINDING LENGTHS Find y. Then find z. Round to the nearest tenth. 42...
 7.7.6.27: FINDING SINE AND COSINE RATIOS Find the unknown side length. Then f...
 7.7.1.27: MULTIPLE CHOICE What is the area of a right triangle with a leg len...
 7.7.7.27: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.27: GRAPHING TRIANGLES Graph points A, B, and C. Connect the points to ...
 7.27: Find sin X and cos X. Write each answer as a fraction, and as a dec...
 7.7.3.27: FINDING LENGTHS Use the Geometric Mean Theorems to find AC and BD. ...
 7.7.4.27: KAYAK RAMP A ramp is used to launch a kayak. What is the height of ...
 7.7.5.28: FINDING LENGTHS Find y. Then find z. Round to the nearest tenth. 30...
 7.7.6.28: ANGLE MEASURE Make a prediction about how you could use trigonometr...
 7.7.1.28: ALGEBRA Solve for x if the lengths of the two legs of a right trian...
 7.7.7.28: CALCULATOR Let A be an acute angle in a right triangle. Approximate...
 7.7.2.28: GRAPHING TRIANGLES Graph points A, B, and C. Connect the points to ...
 7.28: Find sin X and cos X. Write each answer as a fraction, and as a dec...
 7.7.3.28: CHALLENGE Draw a right isosceles triangle and label the two leg len...
 7.7.4.28: DRAWBRIDGE Each half of the drawbridge is about 284 feet long, as s...
 7.7.5.29: FINDING LENGTHS Find y. Then find z. Round to the nearest tenth. 45...
 7.7.6.29: MULTIPLE CHOICE In nJKL, m L 5 908. Which statement about nJKL cann...
 7.7.1.29: CHALLENGE In Exercises 29 and 30, solve for x. 399103
 7.7.7.29: MULTIPLE CHOICE Which additional information would not be enough to...
 7.7.2.29: ALGEBRA Tell whether a triangle with side lengths 5x, 12x, and 13x ...
 7.29: Find sin X and cos X. Write each answer as a fraction, and as a dec...
 7.7.3.29: DOGHOUSE The peak of the doghouse shown forms a right angle. Use th...
 7.7.4.29: SHORT RESPONSE Describe two ways to show that all isosceles right t...
 7.7.5.30: CHALLENGE Find the perimeter of the figure at the right, where AC 5...
 7.7.6.30: PERIMETER Find the approximate perimeter of the figure. 5581.5 cm 6...
 7.7.1.30: CHALLENGE In Exercises 29 and 30, solve for x. 3 1514
 7.7.7.30: WRITING Explain why it is incorrect to say that tan21 x 5 } 1 tan x .
 7.7.2.30: USING DIAGRAMS In Exercises 30 and 31, copy and complete the statem...
 7.30: Solve the right triangle. Round decimal answers to the nearest tent...
 7.7.3.30: MONUMENT You want to determine the height of a monument at a local ...
 7.7.4.30: PROVING THEOREM 7.8 Write a paragraph proof of the 458458908 Tria...
 7.7.5.31: WASHINGTON MONUMENT A surveyor is standing 118 feet from the base o...
 7.7.6.31: PERIMETER Find the approximate perimeter of the figure. .2 cm 1.5 c...
 7.7.1.31: BASEBALL DIAMOND In baseball, the distance of the paths between eac...
 7.7.7.31: SPECIAL RIGHT TRIANGLES If sin A 5 1 }2 } 2 , what is m A? If sin B...
 7.7.2.31: USING DIAGRAMS In Exercises 30 and 31, copy and complete the statem...
 7.31: Solve the right triangle. Round decimal answers to the nearest tent...
 7.7.3.31: SHORT RESPONSE Paul is standing on the other side of the monument i...
 7.7.4.31: EQUILATERAL TRIANGLE If an equilateral triangle has a side length o...
 7.7.5.32: ROLLER COASTERS A roller coaster makes an angle of 528 with the gro...
 7.7.6.32: CHALLENGE Let A be any acute angle of a right triangle. Show that (...
 7.7.1.32: APPLE BALLOON You tie an apple balloon to a stake in the ground. Th...
 7.7.7.32: TRIGONOMETRIC VALUES Use the Table of Trigonometric Ratios on page ...
 7.7.2.32: OPENENDED MATH The side lengths of a triangle are 6, 8, and x (whe...
 7.32: Solve the right triangle. Round decimal answers to the nearest tent...
 7.7.3.32: PROVING THEOREM 7.1 Use the diagram of nABC. Copy and complete the ...
 7.7.4.32: PROVING THEOREM 7.9 Write a paragraph proof of the 308608908 Tria...
 7.7.5.33: CLASS PICTURE Use this information and diagram for Exercises 33 and...
 7.7.6.33: AIRPLANE RAMP The airplane door is 19 feet off the ground and the r...
 7.7.1.33: SHORT RESPONSE Three side lengths of a right triangle are 25, 65, a...
 7.7.7.33: CHALLENGE The perimeter of rectangle ABCD is 16 centimeters, and th...
 7.7.2.33: ALGEBRA The sides of a triangle have lengths x, x 1 4, and 20. If t...
 7.33: Find the measures of GED, GEF, and EFG. Find the lengths of }EG , }...
 7.7.3.33: MULTISTEP PROBLEM Use the diagram. a. Name all the altitudes in nE...
 7.7.4.33: MULTISTEP PROBLEM You are creating a quilt that will have a tradit...
 7.7.5.34: CLASS PICTURE Use this information and diagram for Exercises 33 and...
 7.7.6.34: BLEACHERS Find the horizontal distance h the bleachers cover. Round...
 7.7.1.34: MULTISTEP PROBLEM In your town, there is a field that is in the sh...
 7.7.7.34: SOCCER A soccer ball is placed 10 feet away from the goal, which is...
 7.7.2.34: CHALLENGE The sides of a triangle have lengths 4x 1 6, 2x 1 1, and ...
 7.7.3.34: EXTENDED RESPONSE Use the diagram. a. Sketch the three similar tria...
 7.7.4.34: EXTENDED RESPONSE Use the figure at the right. You can use the fact...
 7.7.5.35: SHORT RESPONSE Write expressions for the tangent of each acute angl...
 7.7.6.35: SHORT RESPONSE You are flying a kite with 20 feet of string extende...
 7.7.1.35: MULTIPLE REPRESENTATIONS As you are gathering leaves for a science ...
 7.7.7.35: SHORT RESPONSE You are standing on a footbridge in a city park that...
 7.7.2.35: PAINTING You are making a canvas frame for a painting using stretch...
 7.7.3.35: PROVING THEOREMS In Exercises 3537, use the diagram and GIVEN state...
 7.7.4.35: CHALLENGE In quadrilateral QRST, mR 5 608, mT 5 908, QR 5 RS, ST 5 ...
 7.7.5.36: EYE CHART You are looking at an eye chart that is 20 feet away. You...
 7.7.6.36: MULTISTEP PROBLEM You want to hang a banner that is 29 feet tall f...
 7.7.1.36: SHORT RESPONSE Justify the Distance Formula using the Pythagorean T...
 7.7.7.36: CLAY In order to unload clay easily, the body of a dump truck must ...
 7.7.2.36: WALKING You walk 749 feet due east to the gym from your home. From ...
 7.7.3.36: PROVING THEOREMS In Exercises 3537, use the diagram and GIVEN state...
 7.7.4.36: In the diagram, ] BD is the perpendicular bisector of}AC . (p. 303)...
 7.7.5.37: EXTENDED RESPONSE According to the Americans with Disabilities Act,...
 7.7.6.37: SHORT RESPONSE Nick uses the equation sin 498 5 x }16 to find BC in...
 7.7.1.37: PROVING THEOREM 4.5 Find the HypotenuseLeg (HL) Congruence Theorem...
 7.7.7.37: REASONING For nABC shown, each of the expressions sin 21 } BC AB , ...
 7.7.2.37: MULTISTEP PROBLEM Use the diagram shown. a. Find BC. b. Use the Co...
 7.7.3.37: PROVING THEOREMS In Exercises 3537, use the diagram and GIVEN state...
 7.7.4.37: In the diagram, ] BD is the perpendicular bisector of}AC . (p. 303)...
 7.7.5.38: CHALLENGE The road salt shown is stored in a coneshaped pile. The ...
 7.7.6.38: TECHNOLOGY Use geometry drawing software to construct an angle. Mar...
 7.7.1.38: CHALLENGE Trees grown for sale at nurseries should stand at least f...
 7.7.7.38: MULTISTEP PROBLEM You are standing on a plateau that is 800 feet a...
 7.7.2.38: SHORT RESPONSE You are setting up a volleyball net. To stabilize th...
 7.7.3.38: CHALLENGE The harmonic mean of a and b is 2ab }}} a 1 b . The Greek...
 7.7.4.38: In the diagram, ] BD is the perpendicular bisector of}AC . (p. 303)...
 7.7.5.39: The expressions given represent the angle measures of a triangle. F...
 7.7.6.39: MULTIPLE REPRESENTATIONS You are standing on a cliff 30 feet above ...
 7.7.1.39: Evaluate the expression. (p. 874) 1}7 22
 7.7.7.39: MULTIPLE REPRESENTATIONS A local ranch offers trail rides to the pu...
 7.7.2.39: EXTENDED RESPONSE You are considering buying a used car. You would ...
 7.7.3.39: Simplify the expression. (p. 874) }27 p }2
 7.7.4.39: Is it possible to build a triangle using the given side lengths? (p...
 7.7.5.40: The expressions given represent the angle measures of a triangle. F...
 7.7.6.40: ALGEBRA If nEQU is equilateral and nRGT is a right triangle with RG...
 7.7.1.40: Evaluate the expression. (p. 874) 14}3 22
 7.7.7.40: OPENENDED MATH Describe a realworld problem you could solve using...
 7.7.2.40: PROVING THEOREM 7.3 Copy and complete the proof of Theorem 7.3. GIV...
 7.7.3.40: Simplify the expression. (p. 874) }8 p }10
 7.7.4.40: Is it possible to build a triangle using the given side lengths? (p...
 7.7.5.41: The expressions given represent the angle measures of a triangle. F...
 7.7.6.41: CHALLENGE Make a conjecture about the relationship between sine and...
 7.7.1.41: Evaluate the expression. (p. 874) 126}81 22
 7.7.7.41: EXTENDED RESPONSE Your town is building a wind generator to create ...
 7.7.2.41: PROVING THEOREM 7.4 Prove Theorem 7.4. Include a diagram and GIVEN ...
 7.7.3.41: Simplify the expression. (p. 874) }12 p }7
 7.7.4.41: Is it possible to build a triangle using the given side lengths? (p...
 7.7.5.42: Copy and complete the statement with <, >, or 5. Explain. (p. 335) ...
 7.7.6.42: Rewrite the equation so that x is a function of y. (p. 877) y 5 }x
 7.7.1.42: Evaluate the expression. (p. 874) 128}2 22
 7.7.7.42: CHALLENGE Use the diagram of nABC. GIVEN c nABC with altitude }CD ....
 7.7.2.42: PROVING THEOREM 7.2 Prove the Converse of the Pythagorean Theorem. ...
 7.7.3.42: Simplify the expression. (p. 874) }18 p }12
 7.7.4.42: Tell whether the given side lengths form a right triangle. (p. 441)...
 7.7.5.43: Copy and complete the statement with <, >, or 5. Explain. (p. 335) ...
 7.7.6.43: Rewrite the equation so that x is a function of y. (p. 877) y 5 3x ...
 7.7.1.43: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.43: Copy and complete the table. (p. 42) Number of sides Type of polygo...
 7.7.2.43: SHORT RESPONSE Explain why D must be a right angle. 06 9CDB EA
 7.7.3.43: Simplify the expression. (p. 874) 5}7
 7.7.4.43: Tell whether the given side lengths form a right triangle. (p. 441)...
 7.7.5.44: Copy and complete the statement with <, >, or 5. Explain. (p. 335) ...
 7.7.6.44: Rewrite the equation so that x is a function of y. (p. 877) y 5 x}9
 7.7.1.44: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.44: A point on an image and the transformation are given. Find the corr...
 7.7.2.44: COORDINATE PLANE Use graph paper. a. Graph nABC with A(27, 2), B(0,...
 7.7.3.44: Simplify the expression. (p. 874) 8}11
 7.7.4.44: Tell whether the given side lengths form a right triangle. (p. 441)...
 7.7.5.45: Find the unknown side length of the right triangle. (p. 433) 18 x24
 7.7.6.45: Copy and complete the table. (p. 884) }x? 0? 1? }2? 2? 4
 7.7.1.45: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.45: A point on an image and the transformation are given. Find the corr...
 7.7.2.45: CHALLENGE Find the values of x and y. 3 35 5 4
 7.7.3.45: Simplify the expression. (p. 874) 15}27
 7.7.5.46: Find the unknown side length of the right triangle. (p. 433) x157
 7.7.6.46: Copy and complete the table. (p. 884) x 1}x? 1? 1}2? 3? 2}7? 7
 7.7.1.46: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.46: A point on an image and the transformation are given. Find the corr...
 7.7.2.46: In Exercises 4648, copy the triangle and draw one of its altitudes....
 7.7.3.46: Simplify the expression. (p. 874) 12}24
 7.7.5.47: Find the unknown side length of the right triangle. (p. 433) x13
 7.7.6.47: Copy and complete the table. (p. 884) x 2}7 x 1 4? 0? 2? 6? 8? 10
 7.7.1.47: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.47: Draw a dilation of the polygon with the given vertices using the gi...
 7.7.2.47: In Exercises 4648, copy the triangle and draw one of its altitudes....
 7.7.3.47: Tell whether the lines through the given points are parallel, perpe...
 7.7.6.48: Find the values of x and y in the triangle at the right. (p. 449) x...
 7.7.1.48: Describe the possible lengths of the third side of the triangle giv...
 7.7.7.48: Draw a dilation of the polygon with the given vertices using the gi...
 7.7.2.48: In Exercises 4648, copy the triangle and draw one of its altitudes....
 7.7.3.48: Tell whether the lines through the given points are parallel, perpe...
 7.7.1.49: Determine whether the two triangles are similar. If they are simila...
 7.7.2.49: Copy and complete the statement. (p. 364) If 10}x 5 7}y, then 10}7 ...
 7.7.3.49: Tell whether the lines through the given points are parallel, perpe...
 7.7.1.50: Determine whether the two triangles are similar. If they are simila...
 7.7.2.50: Copy and complete the statement. (p. 364) f x}15 5 y}2 , then x}y 5...
 7.7.2.51: Copy and complete the statement. (p. 364) If x}8 5 y}9 , then x}1 8...
 7.7.2.52: The perimeter of a rectangle is 135 feet. The ratio of the length t...
Solutions for Chapter 7: Apply the Pythagorean Theorem
Full solutions for Geometry (Holt McDougal Larson Geometry)  1st Edition
ISBN: 9780618595402
Solutions for Chapter 7: Apply the Pythagorean Theorem
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Geometry (Holt McDougal Larson Geometry), edition: 1. Geometry (Holt McDougal Larson Geometry) was written by and is associated to the ISBN: 9780618595402. Since 371 problems in chapter 7: Apply the Pythagorean Theorem have been answered, more than 29100 students have viewed full stepbystep solutions from this chapter. Chapter 7: Apply the Pythagorean Theorem includes 371 full stepbystep solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.