Name: ________________________ Class: ___________________ Date: __________
ID: A
Laws of Sines and Cosines Test Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Find x. Round the result to the nearest hundredth.
a. x = 16.58 b. x = 17.57 c. x = 13.24 d. x = 29.19
2. Write cos x as a fraction in lowest terms.
a.
3
3
4
1
b.
c.
d. 1
4
5
5
4
3. Three ships are at sea: the Admiral, the Barstow, and the Cauldrew. The crew on the Admiral can see both the
Barstow and the Cauldrew. They measure the angle between the line of sight to the Barstow and the line of sight
to the Cauldrew as 31°. They radio the Barstow and by comparing known landmarks, find that the distance
between the Admiral and the Barstow is 402 meters. The Barstow reports that an angle of 70° is found between
their line of sight to the Admiral and their line of sight to the Cauldrew. To the nearest meter, what is the distance
between the Barstow and the Cauldrew?
a. 38 meters b. 211 meters c. 220 meters d. 133 meters
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Name: ________________________
ID: A
4. Solve the triangle for angle A. Then find its area.
a. A = 25.02°, Area = 70 in. 2 b. A = 26°, Area = 70 in. 2 c. A = 25.02°, Area = 67.99 in. 2
d. A = 26°, Area = 67.99 in. 2
Short Answer
5. Write sin A as a fraction in lowest terms.
Use the right triangle to write the quantity as a fraction in lowest terms.
6.
tan P
7. Find x to the nearest hundredth.
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Name: ________________________
ID: A
8. Solve for x to the nearest degree.
Use a calculator. Round to three decimal places.
9. sec 27°
10. csc 20°
11. tan17°
Find the values of x and y.
12.
13. Solve ∆ABC using the diagram and the given measurements. (The triangle is not drawn to scale.)
B = 42°, a = 17
14. A ladder 12 feet long makes an angle of 67° with the ground as it leans against a store. How far up the side of the
store does the ladder reach?
15. A slide 2.8 m long makes an angle of 29° with the ground. How high is the top of the slide above the ground?
16. Given triangle ABC with a = 3, A = 40°, and B = 27°, find c. Round your answer to two decimal places.
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Name: ________________________
ID: A
17. Solve triangle ABC given that A = 47°, B = 52°, and b = 78.
18. Given triangle ABC with a = 10, b = 13, and A = 19°, find c. Round your answer to two decimal places.
19. Find the area of ∆ABC . The figure is not drawn to scale.
20. Find the area of ∆ABC . The figure is not drawn to scale.
21. Solve ∆ABC with A = 110°, a = 5, and b = 7.3.
22. Given triangle ABC with b = 8, c = 5, and A = 58°, find a. Round the answer to two decimal places.
23. Solve triangle ABC given that a = 19, b = 10, and c = 14.
A 50-foot ramp makes an angle of 4.9° with the horizontal. To meet new accessibility guidelines, a new
ramp must be built so it makes an angle of 2.7° with the horizontal.
24. What will be the length of the new ramp?
Other
25. Writing: Explain the difficulties that arise when using SSA information to solve a triangle.
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