Related Rates - Unsure about solution

[carlodelmundo]

Homework Statement

A Missile rises vertically from a point on the ground 75,000 feet from a radar station. If the missle is rising at the rate of 16,500 feet per minute at the instant when it is 38,000 feet high. What is the rate of change, in radians per minute, of the missile's angle of elevation from the radar station at this instant?

A) 0.175
B) 0.219
C) 0.227
D) 0.469
E) 0.507

The Attempt at a Solution

Here's my attempted drawing:

http://carlodm.com/calc/PIC.JPG

I'm thinking of using cosine... but what good does this do me? I'm so lost. Can I get hints please?

 

[Dick]

You should move your radar station down to ground level, where the missile was launched from. And the angle theta they are talking about is the angle at the radar station. Now write down the relation between Y and theta. It isn't cosine. Now find dY/dt in terms of dtheta/dt.

 

[carlodelmundo]

Thank You Dick.

I've solved the problem. I was a little confused about the satellite station... I overlooked that it could be on the ground! For anyone's use I did the following:

tan [theta] = y / 75,000

sec^2 [theta] d[theta]/dt = (1 / 75,000) dy/dt.

I solved for d[theta]/dt and got a result of .175 radians/min. (I solved for cos^2 [theta] by using the Pythagorean theorem with sides a = 75,000 and b = 38,000)

Thanks Dick!