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NemiM [27]
3 years ago
9

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?
Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
6 0

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

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