Question

A construction worker lowers a 100-foot rope from the top of a building. Another worker attaches the bottom of the rope to the ground, 23 feet from the base of the building. What is the height of the building rounded to the nearest foot?

Answer 1

97 ft

Explanation:

The Pythagorean theorem is useful for working problems like this. It tells you the relationship between side lengths and the hypotenuse of a right triangle.

Here, the building is presumed to be perpendicular to the ground, so the 100' rope is the hypotenuse of a triangle with legs equal to 23' and the height of the building (b).

23² +b² = 100²

b = √(10000 -529) ≈ 97.32

The height of the building is about 97 feet.