A plane flying horizontally at an altitude of 4 mi and a speed of 465 mi/h passes directly over a radar statio

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

Let R be the radar station , S the point 4 mi vertically above R and the plane P
x mi horizontally from S. You are given that dx/dt = 465.
You want d(RP)/dt and this = dx/dt(cos(SPR).
cos(SPR)=x/RP=x/10 and when PR=10, x=sqrt(10^2-4^2)=sqrt(84)
so cos(SPR)=[sqrt(84)]/10
Answer = 465[sqrt(84)]/10 mi/h which I will leave you to round .

You can also do from d(RP)/dt = d[sqrt(x^2+16)]/dt but it is a little more
complicated.