Question

A ladder leans against the wall of a building. The ladder measures

55 inches and forms an angle of 63 with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.

Answer 1

We can use trigonometry to solve this problem. Let's label the height of the building (the distance from the ground to the point where the ladder touches the wall) as h, and the distance from the wall to the base of the ladder as x. We can use the sine and cosine functions to set up two equations:

sin(63) = h/55 (since sine is opposite/hypotenuse)
cos(63) = x/55 (since cosine is adjacent/hypotenuse)

Solving for h, we get:

h = 55 sin(63) ≈ 50.38 inches

Solving for x, we get:

x = 55 cos(63) ≈ 26.87 inches

Therefore, the top of the ladder is approximately 50.38 inches from the ground, and the base of the ladder is approximately 26.87 inches from the wall.