Use the Law of Cosines to find the missing angle. In triangle FGH, HF = 16 ft, FG = 23 ft, and m∠F = 52°. Find the measure of f. Round your answer to the nearest whole number.

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27-04-2018
Mathematics

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Use the Law of Cosines to find the missing angle. In triangle FGH, HF = 16 ft, FG = 23 ft, and m∠F = 52°. Find the measure of f. Round your answer to the nearest whole number.

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MsEHolt MsEHolt · Answer 1 · 2018-05-08T05:26:58+02:00

MsEHolt MsEHolt

08-05-2018

f = 18 ft.

The law of cosines states
c² = a² + b² - 2ab cos C

Using our information, we have
c² = 23² + 16² - 2(23)(16)cos 52
c² = 529 + 256 - 736cos 52
c² = 785 - 736cos 52
c² = 331.8732

Taking the square root of both sides, we have
c = √331.8732 = 18.22 ≈ 18

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