Question

A 15-ft ladder is propped against a vertical wall and makes a 72 ̊ angle with the ground. How far is the foot of the ladder from the base of the wall? Round to the nearest tenth.

Answer 1

We first approach this problem by illustrating the situation. Refer to the diagram attached.

From the diagram, we can clearly see that we need to simply solve for the length marked x in order to find the distance between the foot of the ladder to the base of the wall.

Remember SOHCAHTOA. We can apply here the concept of cosine since we have the angle. Incorporationg x into the equation, we can simply make use of the relation cosine 72° = adjacent/hypotenuse.

$cos(72deg)= \frac{x}{15}$
$15cos(72deg)=x$
$x=4.6$

ANSWER: The distance between the foot of the ladder and the base of the wall is 4.6 feet.