To find the length of HG, we can use the Law of Cosines:
HG^2 = FH^2 + FG^2 - 2(FH * FG * cos(m∠F))
HG^2 = 8^2 + 13^2 - 2(8 * 13 * cos(72))
HG^2 = 64 + 169 - 2(8 * 13 * cos(72))
HG^2 = 233 - 208 * cos(72)
Now we need to find the cosine of 72 degrees, which is equal to 0.309.
HG^2 = 233 - 208 * 0.309
HG^2 = 233 - 64.272
HG^2 = 168.728
Now find the square root of 168.728 to get HG:
HG = √168.728
HG ≈ 12.98
Round the answer to the nearest whole number: HG ≈ 13ft.
In ΔFGH, FH = 8ft., FG = 13ft., and m∠F = 72°
Find the length of HG. Round your answer to the nearest whole number.
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