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.

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

Yes, two vertical lines can be complementary