Related Rates Calculus (Implicit Differentiation)

Question

Herman is cleaning the exterior of a glass building with a squeegee. The base of the 10 foot long squeegee handle, which is resting on the ground, makes an angle of A with the horizontal. The top of the squeegee is x feet above the ground on the building. Herman pushes the bottom of the squeegee handle toward the wall. Find the rate at which x changes with respect to A when A=60 degrees. Express the answer in feet per degree.

Answer 1

Draw right triangle. The hypotenuse is the handle. The vertical leg is the height x. The horizontal leg is the ground.

 

Then in feet, x = 10 sin A.

 

Thus in feet per radian, dx/dA = 10 cos A

 

For if A = 60° = π/3 radians, this is 10 cos(π/3) = 5 feet per radian.

 

There are 180 degrees in π radians so the rate in feet per degree is

 

5π/180 = 0.087266...