We first want to use the Law of Cosines to find the length of HG.
The Law of Cosines states that for any triangle with sides of length a, b, and c and opposite angle of A, B, and C respectively the following holds true:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our triangle, we have:
a = FH = 8ft.
b = FG = 13ft.
C = m∠F = 72°
We want to find c = HG. Plugging in our values, we get:
HG^2 = 8^2 + 13^2 - 2(8)(13) * cos(72°)
HG^2 = 64 + 169 - 208 * cos(72°)
HG^2 ≈ 233 - 208 * 0.3090
HG^2 ≈ 233 - 64.2752
HG^2 ≈ 168.7248
Now we take the square root of both sides to find HG:
HG ≈ √168.7248
HG ≈ 12.98
The length of HG is approximately 12.98 feet.
In ΔFGH, FH = 8ft., FG = 13ft., and m∠F = 72°
Find the length of HG.
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