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# The Law of Cosines Practice Questions

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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.

 1 2 3 4 5 6 7 8 9 10 11 12

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

 13 14 15 16 17 18 19 20 21 22 23 24

Find the two possible lengths for the sides labeled x.

 25 26 27

 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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