Algebra II Honors Trig Test #2
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Algebra II Honors Trig Test #2
Multiple Choice Identify the choice that best completes the statement or answers the question.
Simplify the trigonometric expression.
____ 1. a. tan b. 1 c. cot d. sin
Solve the equation for 0 < 2. Write your answer as a multiple of , if possible.
____ 2. 4cos 1 2cos a. b. c. d.
____ 3. a. c.
b. d.
____ 4. a. c.
b. d.
____ 5. a. b. c. d.
____ 6. The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 25° angle with the water. To the nearest foot, how far is the boat from the cliff?
35 ft
25 o 25 ft
Drawing is not to scale. a. 141 feet b. 128 feet c. 27 feet d. 75 feet
____ 7. In XYZ, Y is a right angle and . Find cos X in fraction and in decimal form. Round to the nearest hundredth, if necessary.
Z
25 20
X Y
a. b. c. d.
____ 8. In XYZ, Y is a right angle and . Find sin Z in fraction and in decimal form. Round to the nearest hundredth, if necessary.
Z
5 4
X Y
a. b. c. d.
Find the length x. Round to the nearest tenth.
59 x ____ 9.
55 ° a. 33.8 b. 48.3 c. 84.3 d. 72.0
87 ____ 10.
25° x
a. 78.8 b. 36.8 c. 40.6 d. 205.9
x ____ 11.
42° 80
a. 88.8 b. 72.0 c. 59.5 d. 53.5
10 x ____ 12. 20 °
a. 3.4 b. 9.4 c. 3.6 d. 6.6 ____ 13. In , is a right angle. Find to the nearest tenth of a degree. B x
64.6 60
A 24 C
a. 20.4 b. 68.2 c. 42.9 d. 21.8 ____ 14. Find the measure of x in the right triangle. 8
x 21
a. 22.4° b. 67.6° c. 20.9° d. 69.1° ____ 15. Find the area of the triangle. Round your answer to the nearest tenth.
B
4 m
49°
A 4 m C
a. 9.2 m2 b. 6.0 m2 c. 8 m2 d. 12.1 m2 ____ 16. Use the Law of Sines. Find b to the nearest tenth.
C
31 b
42° 64° B A
a. 47.3 b. 41.6 c. 18.6 d. 23.1 ____ 17. Use the Law of Sines. Find to the nearest tenth. C
69
67° B 72 A
a. 106.2 b. 118.1 c. 61.9 d. 73.8
Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth.
____ 18. = 55°, = 44°, and b = 68 a. = 81°, a = 96.7, c =80.2 c. = 81°, a = 89.2, c = 57.7 b. = 81°, a = 80.2, c = 96.7 d. = 81°, a = 57.7, c =89.2 ____ 19. a = 11, b = 12, and c = 17 a. = 84.8°, = 49.9°, = 45.3° b. = 44.7°, = 40.1°, = 95.2° c. = 84.8°, = 45.3°, = 49.9° d. = 40.1°, = 44.7°, = 95.2° ____ 20. Use the Law of Cosines. Find b to the nearest tenth.
C
60 b
48° B 85 A
a. 102.2 b. 62.4 c. 132.9 d. 63.2 ____ 21. In , j = 9 in., k = 5 in., and = 43°. Find . a. 28° b. 59° c. 32° d. 75° ____ 22. Identify the expression that completes the equation so that it is an identity. = a. b. c. d.
In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
____ 23. a = 3, c = 19 a. = 9.1°, = 80.9°, b = 18.8 c. = 14.5°, = 75.5°, b = 18.8 b. = 80.9°, = 9.1°, b = 18.8 d. = 75.5°, = 14.5°, b = 18.8
Short Answer
Verify the identity. Justify each step.
24. Algebra II Honors Trig Test #2 Answer Section
MULTIPLE CHOICE
1. B 2. A 3. B 4. C 5. D 6. B 7. C 8. B 9. B 10. A 11. B 12. A 13. D 14. B 15. B 16. D 17. D 18. B 19. D 20. D 21. D 22. A 23. A
SHORT ANSWER
24.
tangent identity and cotangent identity
= Write the fractions with a common denominator.
= Add.
= Pythagorean identity