Question

A 13
​-foot
ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 6

feet from the base of the building. How high up the wall does the ladder​ reach?

Answer 1

We can use the Pythagorean theorem to solve this problem. Let's label the height up the wall that the ladder reaches as "x". Then we have:

a = 6 feet (the distance from the base of the building to the bottom of the ladder)
b = x feet (the height up the wall that the ladder reaches)
c = 13 feet (the length of the ladder)

According to the Pythagorean theorem, a^2 + b^2 = c^2. Substituting in our values gives us:

6^2 + x^2 = 13^2
36 + x^2 = 169
x^2 = 133
x ≈ 11.54

So the ladder reaches a height of approximately 11.54 feet up the wall.