Calculus related rates

Question

 A plane flying horizontally at an altitude of 4 mi and a speed of 465 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 10 mi away from the station. Round the result to the nearest integer.

Answer 1

altitude of 4 miles high, 465 miles per hour 10 miles past the radar station

construct a right triangle with height 4, base = 10, d = distance between the plane and the station

d^2 = h^2 + b^2

take the derivative

2dd' = 2hh' +2bb'

divide by 2d

d' = (hh'+bb')/d

plug in values h=4, b=10, h'=0, b' = 465, d =sqr(110)

d' = (4650)/sqr110 = about 443.36 mph = about 443 mph