Question

The recommended angle for a firefighting ladder is 75 degrees. When a 110-foot ladder is put up against a building at this angle, the base of the ladder is about 28 feet from the building. The base of the ladder is 8 feet above the ground. How high on the building will the ladder reach?

Answer 1

Answer: 114.37 ft

Explanation:

If we model this situation as a right triangle, where the hypotenuse is the length of the ladder (
`110 ft`), the opposite leg is the height the ladder will reach
`h`, and the adjacent leg is the distance between the base of the ladder and the building (
`28 ft`); we have two options:

1) Using trigonometric functions, since we are given the angle
`\theta=75\°`

2) Using the Pithagorean Theorem

Any of the options will give a similiar result. So, let's choose the Pithagorean Theorem:

`(hypotenuse)^(2)=(opposite-leg)^(2)+(adjacent-leg)^(2)`

`(110 ft)^(2)=(h)^(2)+(28 ft)^(2)`

Isolating
`h`:

`h=\sqrt{(110 ft)^(2)-(28 ft)^(2)}`

`h=106.37 ft`

Adding to this height the extra height of
`8 ft` (since the base of the ladder is at this distance above the ground, perhaps held by a firefighter truck):

`h=106.37 ft+8 ft=114.37 ft` This is the height the ladder will reach