The Pythagorean Theorem (\(a^{2} + b^{2} = c^{2}\)) can be used to solve this problem.
We know that the ladder is 15 feet in length, and is leaning on a wall from 5 feet away. To work this out, we simply need to figure out which side is the hypotenuse.
The hypotenuse of a right triangle is always the side opposite of the right (90°) angle. In this case, the right angle is that which is made at the wall's intersection with the ground.
In the Pythagorean Theorem, c represents the length of the hypotenuse.
So now, we can work out this problem substituting what we know into the theorem.
\((a^{2} + b^{2} = c^{2}) = (c^{2} - a^{2} = b^{2})\)
\(15^{2} -5^{2} = b^{2}\)
\(225 - 25 = b^{2}\)
\(200 = b^{2}\)
So now we have the result for \(b^{2}\). Since 200 isn't a perfect square, we can represent the length of b as \(\sqrt{200}\) which is our answer.
The ladder reaches \(\sqrt{200}\) feet up the wall.
Hope that helped! =)
