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

In this case, the ladder formed a triangle with the wall, you can see it in the attached diagram.
Let the distance of ladder from base of wall = x
Now to find the value of x, we use cosine ratio.
cos ∅= Adjacent / Hypotenuse
Put values
cos72= x/15
15 cos 72 = x
or
x=15 cos 72
x=4.6 ft ( Rounded to nearest tenth)

So, the distance of ladder from base of the wall is 4.6 ft.