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?
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.