Question

A 45 foot ladder is leaning against a building. If the bottom of the ladder is 27 feet from the base of the building, how tall is the building, h, to the nearest foot?

Answer 1

For this case, we have to form a rectangular triangle. Where the hypotenuse is 45 feet and the base of the triangle is 27 feet. We must find the height.

By the Pythagorean theorem, we have that the height is given by:

$h = \sqrt {H ^ 2-b ^ 2}$

Where:

h: Height

H: Hypotenuse

b: Base

Summarizing the values:

$h = \sqrt {45 ^ 2-27 ^ 2}\\h = \sqrt {2025-729}\\h = \sqrt {1296}\\h = 36$

Thus, the height is 36 feet.

Answer:

36 feet.

Answer 2

The night of the building is 52ft