Question

A ladder that is 4.6 m long is leaning against a wall at an angle of 66.0º with respect to the ground. If the base of the ladder is moved 0.31 m away from the wall, how far will the top of the ladder go down?

Answer 1

Answer:

The top of the ladder go down by 0.15 m.

Explanation:

Here we have right angled triangle.

Hypotenuse = 4.6 m

Bottom angle = 66º

Length from ladder bottom to wall bottom = 4.6 cos66 = 1.87 m

Length from ladder top to wall bottom = 4.6 sin66 = 4.20 m

New length from ladder bottom to wall bottom =  1.87 + 0.31 = 2.18 m

By Pythagoras theorem

New length from ladder top to wall bottom is given by

          $\sqrt{4.6^2-2.18^2}=4.05m$

Distance  the top of the ladder go down = 4.20 - 4.05 = 0.15 m