To find the measure of angle G in triangle FGH, we can use the fact that the sum of angles in a triangle is always 180 degrees.
First, we can find the measure of angle H using the fact that the sum of angles in a triangle is 180 degrees:
H = 180 - F - G
H = 180 - 72 - G
H = 108 - G
Next, we can use the Law of Cosines to find the length of side FG:
FG^2 = GH^2 + FH^2 - 2(GH)(FH)cos(F)
FG^2 = 8^2 + 13^2 - 2(8)(13)cos(72)
FG^2 = 169.21
FG ≈ 13.01 ft
Finally, we can use the Law of Cosines again to find the measure of angle G:
cos(G) = (FG^2 + GH^2 - FH^2) / (2(FG)(GH))
cos(G) = (169.21 + 64 - 169) / (2(8)(13))
cos(G) = 0.7686
G ≈ 40.6 degrees
Therefore, the measure of angle G in triangle FGH is approximately 40.6 degrees.