Question

A ladder 9.00 m long leans against the side of a building. if the ladder is inclined at an angle of 75.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

Answer 1

The question describes a right triangle with hypotenuse as 9 and one of the angles as 75 degrees. We are looking for the length of the leg adjacent the given angle 75 degrees.

Recall that:

$\cos{\theta}=\cfrac{adj}{hyp}\\ \\ \Rightarrow\cos75^o=\cfrac{x}{9}\\ \\ \Rightarrow x=9\cos75^o=9(0.2588)=2.3 ft.$