A ladder 10 ft long rests

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 0.5 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? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)

Answer 1

Draw a figure with a right triangle with vertical leg divided into 2 lengths y(on the bottom) and 10-y on the top.

The horizontal leg ix and the and the ladder makes with the ground is θ.

y = x tan θ and x² + y² = 100

Differentiate both of the equations with respect to t, then you will have the information you need to calculate dθ/dt.