In ΔFGH, f = 960 inches, g = 380 inches and h=820 inches. Find the measure of ∠F to the nearest degree.


answer is 100

Answers

Answer 1

The measure of angle F to the nearest degree is approximately 79 degrees.

How to find the angle

To 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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