A balloon rises at the rate of 8 feet per second from a point on the ground 60 feet from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground.
Θ = 22.78 degrees
derivative of tanΘ=y/x:
sec˛Θ(dΘ/dt) = [ (x)(dy/dt) - (y)(dx/dt) / x˛ ]
1.176(dΘ/dt) = [ 60(8) - (25)(19.2) / 60˛ ]
^^I got the dx/dt number, 19.2 by setting up this proportion:
60/x = 25/8
But then I realized that when I solve this: 60(8) - (25)(19.2), I get 0...what am I doing wrong??
**EDIT: Sorry, you're right, I meant dx/dt and dy/dt