In ΔFGH, FH = 8ft, FG = 13ft, and m∠F = 72°

Find the length of HG.
you should get 13

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Please Answer.

1 answer

We can use the Law of Cosines to solve for the length of HG:

c² = a² + b² - 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

In this case, we want to solve for HG (which is the side opposite angle F), so we can label a = FH = 8ft, b = FG = 13ft, and C = m∠F = 72°.

c² = 8² + 13² - 2(8)(13) cos(72°)
c² = 64 + 169 - 208cos(72°)
c² ≈ 169
c ≈ 13

Therefore, the length of HG is approximately 13ft, as we expected.