In ΔFGH, FH = 8ft., FG = 13ft., and m∠F = 72°
Find the length of HG.
Show Work.
Please Answer.
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.