Question

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

33 inches and forms an angle of 58" 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 denote the distance from the ground to the top of the ladder as x and the distance from the wall to the base of the ladder as y.

Using the given information, we know that:

the length of the ladder (hypotenuse) is 33 inches

the angle between the ladder and the ground is 58 degrees

From trigonometry, we have:

sin(58) = x/33 (since sine = opposite/hypotenuse)

cos(58) = y/33 (since cosine = adjacent/hypotenuse)

Solving for x and y:

x = 33sin(58) ≈ 28.62 inches

y = 33cos(58) ≈ 18.70 inches

Therefore, the top of the ladder is about 28.62 inches from the ground, and the base of the ladder is about 18.70 inches from the wall.