A 13​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder​ reach?

Answer 1

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

where a = 10 feet, b = height up the wall, and c = 13 feet (length of the ladder).

Substitute the known values into the equation:

10^2 + b^2 = 13^2
100 + b^2 = 169
b^2 = 169 - 100
b^2 = 69
b = √69
b ≈ 8.31

Therefore, the ladder reaches approximately 8.31 feet up the wall.