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.

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.