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

Step-by-step 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