To find the measure of angle G, we can use the Law of Cosines. Let's call the angle we want to find x.
Using the Law of Cosines:
FH^2 = FG^2 + GH^2 - 2(FG)(GH)cos(x)
Substitute the given values:
8^2 = 13^2 + GH^2 - 2(13)(GH)cos(72°)
64 = 169 + GH^2 - 26GHcos(72°)
Rearranging the equation:
26GHcos(72°) = GH^2 - 105
GH^2 - 26GHcos(72°) - 105 = 0
Using the Law of Cosines:
cos(x) = (FG^2 + GH^2 - FH^2) / 2(FG)(GH)
cos(x) = (13^2 + GH^2 - 8^2) / 2(13)(GH)
cos(x) = (169 + GH^2 - 64) / 26(GH)
cos(x) = (GH^2 - 105) / 26(GH)
Now we have two equations, we can substitute GH^2 - 26GHcos(72°) - 105 for GH^2 in the second equation:
cos(x) = (GH^2 - 105) / 26(GH)
cos(x) = (26GHcos(72°)) / 26(GH)
cos(x) = cos(72°)
x = 72°
Therefore, the measure of angle G is 72°. So, the answer is C. 72.1°.
In ΔFGH, FH = 8 ft, FG = 13 ft, and m∠F = 72°. Find m∠G. Round your answer to the nearest tenth.
A. 26.2º
B. 35.9º
C. 72.1º
D. 32.5º
1 answer