A15-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?

This is the application of trigonometry. The distance of the ladder from from the wall will be given by:
cos θ=(adjacent)/(hypotenuse)
θ=72°
adjacent=base (distance the ladder to base of the wall)= xft
hypotenuse=length of the ladder.
Therefore plugging our values in the formula we get:
cos 72=x/15
x=15 cos 72
x=4.635 ft
Hence we conclude that the foot of the ladder is 4.635 ft away from the base of the wall.