A 20-foot ladder leaning against a wall is used for each a window that is 17 feet above the ground. How far from the wall is the bottom of the ladder?

We know that the building must form a right angle with the ground, so the triangle formed by the ladder, the wall, and the distance between the base of the ladder and the wall is a right triangle. We can use the Pythagorean theorem to find the distance the ladder is from the building.

a^2 + b^2 = c^2

We know that the ladder is the hypotenuse because it is opposite the right angle.

a^2 + b^2 = 20^2

Substitute the length of the other side and solve.

a^2 + 17^2 = 20^2

a^2 + 289 = 400

a^2 = 111

The distance from the wall to the bottom of the ladder is the square root of 111 or approximately 10.5357 feet