Question

Bob is driving along a straight and level road straight toward a mountain. at some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 23 degrees 42 minutes. he then drives 1 mile more and measures the angle of elevation to be 30 degrees 38 minutes. find the height of the mountain to the nearest foot.

Answer 1

Let the height of the mountain (in feet) be H.
Let the initial horizontal distance from the mountain peak be X.
H/X = tan 23.7 = 0.43897
H/(X-5280) = tan 30.633 =0.59218

Solve the two equations in two unknowns (X and H)
H - 0.43897X = 0
H - 0.59218X = -3126.7

Answer 2

20420