To solve this problem, we will use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the unknown side (HG), a and b are the known sides (FH and FG), and C is the angle F. Plugging in the given values, we have:
HG^2 = 8^2 + 13^2 - 2(8)(13) * cos(72)
HG^2 = 64 + 169 - 208 * cos(72) = 233 - 208 * 0.309
HG^2 = 233 - 64.27
HG^2 = 168.73
HG = sqrt(168.73)
HG ≈ 12.99 ft.
So the length of HG is approximately 12.99 feet.
In ΔFGH, FH = 8ft., FG = 13ft., and m∠F = 72°
Find the length of HG.
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