Question

A painter has a 24 foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder sanely reach?

Answer 1

The ladder can reach a height of 22.6 feet.

Explanation:

In order to find the height that the ladder can reach, you need to use the Pythagorean Theorem. The Pythagorean Theorem assumes that the house to the ground will form a right triangle and the leaning ladder is the hypotenuse. Using the formula: a² + b² = c², we can plug in the values that we know and solve for the missing variable. In this case we know the base of the triangle 'b' and the hypotenuse 'c': a² + 8² = 24² or a² + 64 = 576. To solve for a, we must first subtract 64 from both sides: a² + 64 - 64 = 576 - 64 or a² = 512. In order to find just the value of 'a', which represents the height, we need to take the square root of both sides: √a² = √512 or a ≈ 22.6 feet.