The question is as follows: A 10-foot ladder is sliding down a wall. The top of the ladder is moving at a constant rate of 3 feet per second. What is the rate of change in the angle that the ladder makes with the ground when the base of the ladder is 6 feet from the wall?
-5/18 rad/s as my answer but that does not seem to be correct.
x/10 = cos(θ), the first derivative being
d(θ)/dt = dx/dt*(1/-10sin(θ)). Sin(θ) = 8/10 making the full thing
dθ/dt= 3(-1/(10(8/10))) which gives me -5/18 rad/s.
Where am I going wrong?