Question

If you place a 33-foot ladder against the top of a building and the bottom of the ladder is 26 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

Answer 1

20.3 ft

Explanation:

You want to know the height of a building if a 33 ft ladder reaches from the top of the building to a point 26 ft from the bottom of the building.

Right triangle

The geometry can be modeled by a right triangle with hypotenuse 33 ft and one leg of 26 ft. The other leg length (the building height) is found using the Pythagorean theorem.

26² + h² = 33²

h = √(33² -26²) ≈ 20.3 . . . . ft

The building is about 20.3 feet high.

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Additional comment

This ladder makes an angle of about 38° with the ground. For ladder safety, an angle around 70° is usually recommended.

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