Question

A fifteen foot ladder is placed against a wall. It reaches 13 feet up the wall. What is the longest distance away from the wall the ladder can be placed?

Answer 1

Explanation:

The question is phrased oddly, asking “how far *can* the ladder be from the wall,” instead of “how far *is* the ladder from the wall.”

Draw a picture. The 15-foot ladder is the hypotenuse of a right triangle. The vertical leg of the triangle is 13 feet.

By the Pythagorean Theorem, the remaining leg is √(15²-13²) ≈ 7.5 feet.

Note that the ladder *can* be 7.5 feet from the wall, but it *shouldn’t* be. The angle to the ground is 60°, when the recommended angle is 75°. That makes it. 3.9 feet