How far up a wall will a 25 foot long ladder reach if the bottom must be atleast 6 feet from the bottom of the wall ? What will be the slope of the ladder if the bottom is 6 feet from tge wall ?

Question

What angle will the ladder make with the ground ?Please show me step by step. Thank you so much!

Answer 1

The ladder forms the hypotenuse of a right triangle. The height is given by Pythagoras=√(25^2-6^2)=√(625-36)=√589=24.27 feet approx. Depending on the friction of the ladder on the ground, this height will reduce as the ladder moves away from the wall, and increase if the ladder is moved nearer the wall.

The slope is √589/6=4.045 approx. This tangent corresponds to 76.11 degrees.