Question

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 1.2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? Evaluate your answer numerically. (Round the answer to three decimal places.)

Answer 1

Use the Pyth theorem:

10^2=base^2 + height^2 You know the base, find the height.

Now, to work the rates...
take the derivative of the pyth theorem
0=2b db/dt + 2h dh/dt
so dh/dt=-b/h db/dt
Now you know b, h, and db/dt solve for dh/dt.

Answer 2

1.6