1. Use the Law of Sines to find angle C. Let a = 28, and c = 13. a. 24 b. 25 c. 23 d Solve the triangle using the Law of Sines. Let. a. b.

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1 Precalculus with Limits (Larson 2 nd e) Name: Chapter 5.4, 5.5, 6.1 and 6.2 Midterm Exam Review Date: Hour: Multiple Choice Version (Law of Sines, Law of Cosines, Sum & Difference Formulas) Identify the choice that best completes the statement or answers the question. 1. Use the Law of Sines to find angle C. Let a = 28, and c = c Solve the triangle using the Law of Sines. Let. c. 3. Use the Law of Sines to solve for all possible triangles that satisfy a = 23, b = 14, conditions. c. 4. Use the Law of Sines to solve for all possible triangles that satisfy b = 23, c = 35, conditions. c. 5. Use the Law of Cosines to determine side x if b = 9, c = 18, and c. No correct answer

(b) How high is the satellite above the ground? The distance of the satellite from station A = 505.4, the satellite is high above the ground as 503.8.

2 6. The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 51 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be. (a) How far is the satellite from station A? (b) How high is the satellite above the ground? The distance of the satellite from station A = 505.4, the satellite is high above the ground as The distance of the satellite from station A = 525.4, the satellite is high above the ground as c. The distance of the satellite from station A = 511.4, the satellite is high above the ground as The distance of the satellite from station A = 473.4, the satellite is high above the ground as A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, c = 6 mi apart, to be. (a) Find the distance of the plane from point A. (b) Find the elevation of the plane. The distance of the plane from point A = 4.8, the elevation of the plane = 4.4 The distance of the plane from point A = 4.8, the elevation of the plane = 2.2 c. The distance of the plane from point A = 2.2, the elevation of the plane = 2.4 The distance of the plane from point A = 5.9, the elevation of the plane = Find the indicated angle if a = 120, c = 135,. (Use either the Law of Sines or the Law of Cosines, as appropriate.) c. 85

9. Use the Law of Cosines to determine angle if a = 69.19, b = 35.97, c = 42.82. 44.21 25.97 c. No correct answer 63.29 10. Solve triangle ABC, if a = 17, b = 10, and. c = 23.31, c = 23.31, c. c = 28.

3 9. Use the Law of Cosines to determine angle if a = 69.19, b = 35.97, c = c. No correct answer Solve triangle ABC, if a = 17, b = 10, and. c = 23.31, c = 23.31, c. c = 28.31, c = 23.31, 11. Solve triangle ABC if a = 12, b = 18, c = 14. c. 12. Find the indicated side x if b = 6,. (Use either the Law of Sines or the Law of Cosines, as appropriate.) c Two tugboats that are 118 ft apart pull a barge, as shown. If the length of one cable is 206 and the length of the other is 227, find the angle formed by the two cables c

14. A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34.

4 14. A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34. Approximate the distance between the kites ft ft c ft ft 15.Use an addition or subtraction formula to find the exact value of the expression. 16. Use an addition or subtraction formula to find the exact value of the expression. 17. Use an addition or subtraction formula to find the exact value of the expression. 18. Use an addition or subtraction formula to write the expression as a trigonometric function of one number. 19. Use an addition or subtraction formula to write the expression as a trigonometric function of one number.

5 20. Simplify the following expression. cos u cos u c. sin u sin u 21. Simplify the following expression. sin(v + x) sin(v x) 2sin(x)sin(v) 2cos(v)sin(x) c. 2cos(x)sin(v) 2cos(v)cos(x) 22. Simplify the following expression cos(p + z) cos(p z) 2cos(p)cos(z) 2sin(p)sin(z) c. 2sin(p)sin(z) 2cos(p)cos(z) 23. Find the area of the triangle whose sides have the given lengths. a = 4, b = 13, c = Given m B 83, m C 45 and b 89. Find the area of the triangle. 25. Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147, and 190 ft? Please round the answer to the nearest dollar. 26. Find sin(a + B) if cos A = 1, with A in quadrant II, and sin B = Convert each angle to decimal. Round to the nearest hundredth. 1, with B in quadrant IV c, MULTIPLE CHOICE 1.A 2.D 3.B 4.D 5.A 6.A 7.B 8.C 9.B 10.D 11.C 12.C 13.C 14.D 15.C 16.C 17.D 18.B 19. A 20.B 21.B 22.C $87, c

6 Precalculus with Limits (Larson 2 nd e) Chapter 5.5 Midterm Exam Review Double & Half Angles Multiple Choice: Identify the choice that best completes the statement or answers the question. Use a double-angle identity to find the exact value of the expression. 1. cos tan Use identities to write the equation in terms of the single angle. Then solve the equation for 0 2. Use a half-angle identity to find the exact value of the expression. 4. sin cos Given and, find the exact value of Given and, find the exact value of Find the exact values of sin 2A given that tan A = 3 with A in quadrant II c Answers: 1.B 2.C 3.D 4.A 5.B 6.C 7.B 8.D

Test3 Review. $ & Chap. 6. g(x) 6 6cosx. Name: Class: Date:

Test3 Review. $ & Chap. 6. g(x) 6 6cosx. Name: Class: Date: Class: Date: Test Review $5.-5.5 & Chap. 6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Graph the function. g(x) 6 6cosx a. c. b. d. . Graph the function.