Question

A plane flying horizontally at an altitude of 3 mi and a speed of 440 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 4 mi away from the station. (round your answer to the nearest whole number.)

Answer 1

Let α represent the acute angle between the horizontal and the straight line from the plane to the station. If the 4-mile measure is the straight-line distance from the plane to the station, then
sin(α) = 3/4
and
cos(α) = √(1 - (3/4)²) = (√7)/4

The distance from the station to the plane is increasing at a rate that is the plane's speed multiplied by the cosine of the angle α. Hence the plane–station distance is increasing at the rate of
(440 mph)×(√7)/4 ≈ 291 mph