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Chapter 0: Problem 40

The base of a 30 -foot ladder is 10 feet from a building. If the ladder reaches the flat roof, how tall, to the nearest tenth of a foot, is the building?

Short Answer

Expert verified
The height of the building is 28.3 feet.

Step by step solution

01

Identifying the known sides of the triangle

From the problem, it is known that the length of the ladder (hypotenuse) is 30 feet and the distance from the base of the ladder to the building (adjacent side) is 10 feet.
02

Applying the Pythagorean theorem

The opposite side (height of the building) can be calculated using the Pythagorean theorem, i.e., \( Hypotenuse^{2} = Adjacent^{2} + Opposite^{2} \). Thus, the Opposite can be calculated as \( \sqrt{ Hypotenuse^{2} - Adjacent^{2} } \).
03

Calculating the height of the building

By substituting the known values into the Pythagorean theorem: \( Opposite = \sqrt{ 30^{2} - 10^{2} } = \sqrt{ 900 - 100 } = \sqrt{ 800 } = 28.28 \) feet approximately. Rounded to the nearest tenth of a foot, it gives 28.3 feet.

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