Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the equation a/b = c/d for the given variable. a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the equation a/b = c/d for the given variable. b

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the equation a/b = c/d for the given variable. c

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the equation a/b = c/d for the given variable. d

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, evaluate the expression. \(\frac{7 \sin 48^{\circ}}{\sin 23^{\circ}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, evaluate the expression. \(\frac{9 \sin 121^{\circ}}{\sin 14^{\circ}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve for the angle x. \(\sin x=0.3, \quad 0^{\circ}<x<90^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve for the angle x. \(\sin x=0.3, \quad 90^{\circ}<x<180^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve for the angle x. \(\sin x=-0.7, \quad 180^{\circ}<x<270^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, solve for the angle x. \(\sin x=-0.7, \quad 270^{\circ}<x<360^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the triangle.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the triangle.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the triangle.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, solve the triangle.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve the triangle. \(A=40^{\circ}, \quad B=30^{\circ}, \quad b=10\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve the triangle. \(A=50^{\circ}, \quad B=62^{\circ}, \quad a=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve the triangle. \(A=33^{\circ}, \quad B=70^{\circ}, \quad b=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, solve the triangle. \(B=16^{\circ}, \quad C=103^{\circ}, \quad c=12\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, solve the triangle. \(A=32^{\circ}, \quad a=17, \quad b=11\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, solve the triangle. \(A=49^{\circ}, \quad a=32, \quad b=28\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, solve the triangle. \(B=70^{\circ}, \quad b=14, \quad c=9\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, solve the triangle. \(C=103^{\circ}, \quad b=46, \quad c=61\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(A=36^{\circ}, \quad a=2, \quad b=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(B=82^{\circ}, \quad b=17, \quad c=15\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(C=36^{\circ}, \quad a=17, \quad c=16\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(A=73^{\circ}, \quad a=24, \quad b=28\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(C=30^{\circ}, \quad a=18, \quad c=9\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, state whether the given measurements determine zero, one, or two triangles. \(B=88^{\circ}, \quad b=14, \quad c=62\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two triangles can be formed using the given measurements. Solve both triangles. \(A=64^{\circ}, \quad a=16, \quad b=17\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two triangles can be formed using the given measurements. Solve both triangles. \(B=38^{\circ}, \quad b=21, \quad c=25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two triangles can be formed using the given measurements. Solve both triangles. \(C=68^{\circ}, \quad a=19, \quad c=18\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two triangles can be formed using the given measurements. Solve both triangles. \(B=57^{\circ}, \quad a=11, \quad b=10\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Determine the values of b that will produce the given number of triangles if a = 10 and \(B = 42^{\circ}\). (a) Two triangles (b) One triangle (c) Zero triangles

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Determine the values of c that will produce the given number of triangles if b = 12 and \(C = 53^{\circ}\). (a) Two triangles (b) One triangle (c) Zero triangles

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 25 and 26, decide whether the triangle can be solved using the Law of Sines. If so, solve it. If not, explain why not.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 25 and 26, decide whether the triangle can be solved using the Law of Sines. If so, solve it. If not, explain why not.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(A=61^{\circ}, \quad a=8, \quad b=21\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(B=47^{\circ}, \quad a=8, \quad b=21\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(A=136^{\circ}, \quad a=15, \quad b=28\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(C=115^{\circ}, \quad b=12, \quad c=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(B=42^{\circ}, \quad c=18, \quad C=39^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(A=19^{\circ}, \quad b=22, \quad B=47^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(C=75^{\circ}, \quad b=49, \quad c=48\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(A=54^{\circ}, \quad a=13, \quad b=15\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(B=31^{\circ}, \quad a=8, \quad c=11\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2736, respond in one of the following ways: (a) State, Cannot be solved with the Law of Sines. (b) State, No triangle is formed. (c) Solve the triangle. \(C=65^{\circ}, \quad a=19, \quad b=22\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two markers A and B on the same side of a canyon rim are 56 ft apart. A third marker C, located across the rim, is positioned so that \(\angle B A C=72^{\circ}\) and \(\angle A B C=53^{\circ}\). (a) Find the distance between C and A. (b) Find the distance between the two canyon rims.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two meteorologists are 25 mi apart located on an east-west road. The meteorologist at point A sights a tornado \(38^{\circ}\) east of north. The meteorologist at point B sights the same tornado \(53^{\circ}\) west of north. Find the distance from each meteorologist to the tornado. Also find the dista

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A vertical flagpole stands beside a road that slopes at an angle of \(15^{\circ}\) with the horizontal. When the angle of elevation of the Sun is \(62^{\circ}\) , the flagpole casts a 16-ft shadow downhill along the road. Find the height of the flagpole.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Observers 2.32 mi apart see a hot-air balloon directly between them but at the angles of elevation shown in the figure. Find the altitude of the balloon.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A 4-ft airfoil attached to the cab of a truck reduces wind resistance. If the angle between the airfoil and the cab top is \(18^{\circ}\) and angle B is \(10^{\circ}\), find the length of a vertical brace positioned as shown in the figure.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A Ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the observers to the top of the pole are \(19^{\circ}\) and \(21^{\circ}\). Find the height of the flagpole.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two observers are 400 ft apart on opposite sides of a tree. The angles of elevation from the observers to the top of the tree are \(15^{\circ}\) and \(20^{\circ}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two lighthouses A and B are known to be exactly 20 mi apart on a north-south line. A ships captain at S measures \(\angle A S B\) to be \(33^{\circ}\). A radio operator at B measures \(\angle A B S\) to be \(52^{\circ}\). Find the distance from the ship to each lighthouse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A geometry class is divided into ten teams, each of which is given a yardstick and a protractor to find the distance from a point A on the edge of a pond to a tree at a point C on the opposite shore. After they mark points A and B with stakes, each team uses a protractor to measure angles A and B and

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The ratio of the sines of any two angles in a triangle equals the ratio of the lengths of their opposite sides. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The perimeter of a triangle with two 10-inch sides and two \(40^{\circ}\) angles is greater than 36. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice The length x in the triangle shown at the right is (A) 8.6. (B) 15.0. (C) 18.1. (D) 19.2. (E) 22.6.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Which of the following three triangle parts do not necessarily determine the other three parts? (A) AAS (B) ASA (C) SAS (D) SSA (E) SSS

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice The shortest side of a triangle with angles \(50^{\circ}, 60^{\circ}\) and \(70^{\circ}\) has length 9.0. What is the length of the longest side? (A) 11.0 (B) 11.5 (C) 12.0 (D) 12.5 (E) 13.0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice How many noncongruent triangles ABC can be formed if AB = 5, \(A = 60^{\circ}\), and BC = 8? (A) None (B) One (C) Two (D) Three (E) Infinitely many

Precalculus: Graphical, Numerical, Algebraic 8th Edition
(a) Show that there are infinitely many triangles with AAA given if the sum of the three positive angles is \(180^{\circ}\). (b) Give three examples of triangles where \(A = 30^{\circ}, B = 60^{\circ}\), and \(C = 90^{\circ}\). (c) Give three examples where \(A = B = C = 60^{\circ}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the Law of Sines and the cofunction identities to derive the following formulas from right triangle trigonometry: (a) \(\sin A=\frac{o p p}{h y p}\) (b) \(\cos A=\frac{a d j}{h y p}\) (c) \(\tan A=\frac{o p p}{a d j}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Refer to Figures 5.16 and 5.17 in Exploration 1 of this section. (a) Express h in terms of angle A and length AB. (b) In terms of the given angle A and the given length AB, state the conditions on length BC that will result in no triangle being formed. (c) In terms of the given angle A an

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Solve this triangle assuming that \(\angle B\) is obtuse. [Hint: Draw a perpendicular from A to the line through B and C.]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Towers A and B are known to be 4.1 mi apart on level ground. A pilot measures the angles of depression to the towers to be \(36.5^{\circ}\) and \(25^{\circ}\), respectively, as shown in the figure. Find distances AC and BC and the height of the airplane.