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.

Question

anyanavicka [17]

3 years ago

6

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.

Mathematics

1 answer:

ivolga24 [154] · Answer 1 · 2022-03-12T10:55:11+03:00

ivolga24 [154]3 years ago

5 0

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