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# Trigonometry and Triangles Practice Questions

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Updated on Oct 1, 2011

Read the following study guide for a concept review:

Trigonometry and Triangles Study Guide

## Practice Questions

Given two angles of a triangle, find the measure of the third angle.

 1 30° and 45° 2 120° and 14° 3 80° and 80° 4 5 6

Suppose a right triangle has an angle of measure θ, as shown in Figure 2.3. Find the measure of the third angle α.

 7 θ = 30° 8 θ = 45° 9 θ = 15° 10 θ = 11 θ = 12 θ =
 13. One triangle has sides that are 9, 12, and 20 inches in length. Another has sides 18, 24, and 50 inches in length. Are the triangles similar? 14. One triangle has sides 4, 8, and 30 inches in length. Another has sides 6,12, and 45 inches in length. Are the triangles similar? 15. Are these triangles similar (Figure 2.12)? 16. Are these triangles similar (Figure 2.13)?

In problems 17 through 26, find the length x.

 17 18 19 20 21 22 23

 1. 105° 2. 46° 3. 20° 4. 5. 6. 7. α = 60° 8. α = 45° 9. α = 75° 10. α = 11. α = 12. α = 13. No, the triangles are not similar. 14. Yes, the triangles are similar. 15. No. The first triangle has angles 40°, 100°, and 40°, while the second has angles 50°, 100°, and 30°. 16. Yes, the last two angles of the first triangle have the same measure θ because the triangle is isosceles. Thus, , so . Because you have seen that two of the corresponding angles are equal, you know that the triangles are similar. 17. x = 50 18. x = 24 19. 20. x = 42 21. 22. This triangle is similar to any other equilateral triangle, which have all sides of the same length like this one, x = 10. 23. First we figure that the third side of the second triangle is 26. Then we figure that the third triangle's sides are k times those of the second, since they are similar. x = k · 11 40 = k · 26

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