Question

A 10 foot ladder leans against a building that is 8 feet off of the ground. At what height would a 25 foot ladder touch the building if both ladders form the same angle with the ground?

Answer 1

19.99feet

Explanation:

The set up will form a right angles triangle:

First we need to get the angle of elevation of the first ladder using SOH, CAH, TOA

The length of the ladder will be the hypotenuse = 10foot

The opposite will be the height of the building = 8ft

Using Sin(theta) = opposite/hyp

sin Theta = 8/10

theta = sin^{-1}0.8

theta = 53.13°

If the length of the ladder is now 25 foot, the height of the building will be calculated as shown;

sin Theta = h/25

sin53.13 = h/25

h = 25sin53.13

h = 19.99feet

Hence the height of the building will be 19.99feet