Question

A ladder is leaning against a building. The base of the ladder is 57 feet from the bottom of the building. The angle between the ground and the ladder is 55 degrees. What is the length of the ladder from the ground to the top of the building? Round to the nearest tenth. Draw a picture and show all your work.

a) 79.5 feet
b) 65.8 feet
c) 89.2 feet
d) 42.6 feet

Answer 1

The vertical height of the ladder is near c) 89.2 feet

What is the lenght of the lader?

At the end you can see a diagram of the situation, we can model this with a right triangle, and we want to get the height of said triangle.

We have an angle and the adjacent cathetus, then we can use the trigonometric relationship:

tan(angle) = (opposite cathetus)/(adjacent cathetus)

Replacing what we know:

tan(55°) =x/57ft

x = tan(55°)*57 ft = 84.7ft

The closer option to thisone is 89.2ft, which means that some of the numbers in the question must be wrong.