The measure of angle F to the nearest degree is approximately 79 degrees.
How to find the angleTo find the measure of angle F in triangle FGH, we can use the Law of Cosines.
c² = a² + b² - 2ab*cos(C)
In this case, we know that:
FG = 960 inches (side a)
GH = 380 inches (side b)
FH = 820 inches (side c)
We want to find angle F, which is opposite side FG.
Plugging in the values into the Law of Cosines:
FG^2 = FH^2 + GH^2 - 2(FH)(GH)*cos(F)
960^2 = 820^2 + 380^2 - 2(820)(380)*cos(F)
921600 = 672400 + 144400 - 622400*cos(F)
921600 = 816800 - 622400*cos(F)
622400*cos(F) = 921600 - 816800
622400*cos(F) = 104800
cos(F) = 104800 / 622400
cos(F) ≈ 0.1685
Now, to find angle F, we can take the inverse cosine (cos^-1) of 0.1685:
F ≈ cos^-1(0.1685)
F ≈ 79.11 degrees
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