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?

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 (), the opposite leg is the height the ladder will reach , and the adjacent leg is the distance between the base of the ladder and the building (); we have two options:

1) Using trigonometric functions, since we are given the angle

2) Using the Pithagorean Theorem

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

Isolating :

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

This is the height the ladder will reach

your answer would be 10x - 1

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°