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# Note for MATH 1330 at UH

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Date Created: 02/06/15

Exercise Set 71 Solving Right Triangles For each of the following examples a Write a trigonometric equation that can be used to nd x and write a trigonometric equation that can be used to nd y Each equation should involve the given acute angle and the given side length from the diagram Do not solve the equations in this step b Solve the equations from part a to find exact values for x andy c As an alternative solution to the method above use properties of special right triangles from Section 41 to nd exact values ofx and y 1 10 y I x 2 y x I 7 3 y 7J3 I x 4 x y 60 9 5 y 5 a x Math 1330 Precalculus The University of Houston 6 y x 30 15 7 45 7J5 x I y s 45 1 1 x ZI y Use a calculator to evaluate the following Round answers to the nearest tenthousandth 9 a sin48 b cos73 10 a cos16 b tan67 11 a tan b sin 277rj 12 a sin b 00531 71rj In the equations below x represents an acute angle of a triangle Use a calculator to solve for x Round answers to the nearest hundredth of a degree 13 sinx 07481 14 cosx 00256 15 tanx 4 16 tanx Chapter 7 Triganamemc Applications to Tw39zzngles Exercise Set 71 Solving Right Triangles 17 cosx g 18 sinx IIb Find the indicated side or angle measures where angles are measured in degrees Round answers to the nearest hundredth 19 Find x 23 20 Find x 21 In AABC with right angle C 4A 74 and BC 32 in Find AC 22 In AQRS with right angle R QR 7 in and 4Q12 Find QS 23 Find 4H H 17 I 13 I 24 Find 6 4 I 3 Math 1330 Precalculus The University of Houston 25 In AGEO with right angle E GE 9 cm and OE7cmFind 4G 26 In ACAR with right angle R CA 11 in and AR8inFind 4A Solve each of the following triangles ie find all missing side and angle measures where angles are measured in degrees Round all answers to the nearest hundredth 27 J 3 I M D 28 C 7L U 12 B 29 P 8 3 H L 30 T A I I R Chapter 7 Triganamem39c Applications to Tw39zzngles Exercise Set 71 Solving Right Triangles For each of the following examples a b 31 32 33 34 35 36 37 38 39 40 Draw a diagram to represent the given situation Find the indicated measure to the nearest tenth An isosceles triangle has sides measuring 9 inches 14 inches and 14 inches What are the measures of its angles An isosceles triangle has sides measuring 10 inches 7 inches and 7 inches What are the measures of its angles An 8foot ladder is leaned against the side of the house If the ladder makes a 72 angle with the ground how high up does the ladder reach A 14foot ladder is leaned against the side of the house If the ladder makes a 63 angle with the ground how high up does the ladder reach The angle of elevation to the top of a agpole from a point on the ground 40 ft from the base of the agpole is 51 Find the height of the agpole The angle of elevation to the top of a agpole from a point on the ground 18 meters from the base of the agpole is 43 Find the height of the agpole A loading dock is 8 feet high If a ramp makes an angle of 34 with the ground and is attached to the loading dock how long is the ramp A loading dock is 5 feet high If a ramp makes an angle of 25 with the ground and is attached to the loading dock how long is the ramp Silas stands 600 feet from the base of the Sears Tower and sights the top of the tower If the Sears Tower is 1450 feet tall approximate the angle of elevation from Silas perspective as he sights the top of the tower Disregard Silas height in your calculations Mimi is sitting in her boat and sees a lighthouse which is 20 meters tall If she sights the top of the lighthouse at a 32 angle of elevation approximately how far is lLimi s boat from the base of the lighthouse Disregard Mimi s distance from the water in your calculations Math 1330 Precalculus The University of Houston 41 42 43 44 45 46 Jeremy is ying his kite at Lake lLichigan and lets out 200 feet of string If his eyes are 6 feet from the ground as he sights the kite at an 55 angle of elevation how high is the kite Assume that he is holding the kite near his eyes Pam is ying a kite at the beach and lets out 120 feet of string If her eyes are 5 feet from the ground as she sights the kite at a 64 angle of elevation how high is the kite Assume that she is also holding the kite near her eyes Doug is out hiking and walks to the edge of a cliff to enjoy the view He looks down and sights a cougar at a 41 angle of depression If the cliff is 60 meters high approximately how far is the cougar from the base of the cliff Disregard Doug s height in your calculations Juliette wakes up in the morning and looks out her Window into the back yard She sights a squirrel at a 54 angle of depression lf Juliette is looking out the Window at a point which is 28 feet from the ground how far is the squirrel from the base of the house From a point on the ground the angle of elevation to the top of a mountain is 42 Moving out a distance of 150 m on a level plane to another point on the ground the angle of elevation is 33 Find the height of the mountain From a point on the ground the angle of elevation to the top of a mountain is 31 Moving out a distance of 200 m on a level plane to another point on the ground the angle of elevation is 18 Find the height of the mountain Chapter 7 Triganamemc Applications 0 Tw39angles

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