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The Law of Cosines Practice Questions

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Updated on Oct 2, 2011

Read the following study guide for a concept review:

The Law of Cosines Study Guide

Practice Questions

Use the Law of Cosines to find the length x in each triangle.

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Use the Law of Cosines to find the measure of angle x in each triangle.

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Find the two possible lengths for the sides labeled x.

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Answers

1. x = ≈ 11.1 ft.
2. x = ≈ 38.2 cm.
3. x = ≈ 33.8 in.
4. x = ≈ 8.2 m
5. x = ≈ 10.6 ft.
6. x = ≈ 55.8 m
7. x = ≈ 18.3 cm
8. x = ≈ 7.7 ft.
9. x = ≈ 37.1 m
10. x = ≈ 69.7 in.
11. x = ≈ 15 in.
12. x = ≈ 116.8 ft.
13. x = cos–1(0.875) ≈ 29°
14. x = cos–1(0.6875) ≈ 46.6°
15. x ≈ cos–1(–0.3929) ≈ 113.1°
16. x = cos–1(0.859375) ≈ 30.8°
17. x ≈ cos–1(0.3423) ≈ 70°
18. x ≈ cos–1(0.9722) ≈ 13.5°
19. x = cos–1(0.859375) ≈ 30.8°
20. x ≈ cos–1(0.5323) ≈ 57.8°
21. x ≈ cos–1(0.553) ≈ 56.4°
22. x ≈ cos–1(0.2174) ≈ 77.4°
23. x ≈ cos–1(0.6597) ≈ 48.7°
24. x ≈ cos–1(–0.2381) ≈ 103.8°
25. x ≈ 14.67 centimeters or x ≈ 31.29 cm
26. x ≈ 10.63 feet or x ≈ 19.47 ft.
27. x ≈ 21.76 centimeters or x ≈ 48.53 cm
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