Please help i need this by 11:30pm EST

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 0.7 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? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)

Answer 1

With related rate problems, you need a relation between the variables and some constraints. Let's say x is distance from base to wall, y is the height of the ladder along the wall, and θ is the angle that the ladder makes with the floor.

We know that cosθ = x/10 ( we can actually ignore y!)

Take the derivative wrt time:

sinθ dθ/dt = 1/10 dx/dt

At x = 8 sinθ = y/10 = sqrt(10²-8²)/10 = 6/10. You are given dx/dt. solve for dθ/dt