A 10-foot ladder leans against a wall with its foot braced 3 feet from wallÍs base. How far up the wall does the ladder reach?

The answer is √91 feet (which is the same as 9.54 feet).

Imagine this as a right triangle. A length of the foot is actually a hypotenuse (c). The distance from wall's base to the ladder foot is one of the sides of the triangle (let it be a).

So, using the Pythagorean theorem:

c² = a² + b²

It is given:

c = 10 feet

a = 3 feet

b = ?

c² = a² + b²

⇒ 10² = 3² + b²

100 = 9 + b²

b² = 100 - 9 = 91

⇒ b = √b² = √91 ≈ 9.54 feet