A 14-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. How high up the wall does the ladder reach?
We can use the Pythagorean theorem to solve this problem.
Let the height up the wall that the ladder reaches be represented by x.
The ladder, the wall, and the ground form a right triangle. The ladder is the hypotenuse of the triangle, and the base of the wall is one of the legs. Therefore, we can set up the equation using the Pythagorean theorem:
(9)^2 + x^2 = (14)^2
81 + x^2 = 196
Subtract 81 from both sides:
x^2 = 115
Take the square root of both sides:
x = √115 ≈ 10.72 feet
Therefore, the ladder reaches approximately 10.72 feet up the wall.