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.
 
 the angle of ascent θ at which the plane took off is: 
 θ = 2.71 degrees.

16 minutes is correct

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