Related Rates: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?

Answer 1

at the moment in question, we have a 6-8-10 triangle.

You know that

tanθ = y/x = √(100-x^2)/x
or,

x tanθ = √(100-x^2)
So,
tanθ dx/dt + x sec^2θ dθ/dt = -x/y dx/dt

Now just plug in your values to find dθ/dt

Answer 2

-.72