Question

An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.

Answer 1

First we convert everything to the same unit taking into account the following conversion:
1 mile = 5280 feet
So, we have:
h = 500 feet
d = 2 (5280) = 10560 feet
Substituting in the given formula we have:
h = d tan θ
500 = 10560tan θ
tan θ = 500/10560
θ = Atan (500/10560)
θ = 2.71 degrees.
Answer:
the angle of ascent θ at which the plane took off is:
θ = 2.71 degrees.