The Pythagorean Theorem (

) 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.



So now we have the result for

. Since 200 isn't a perfect square, we can represent the length of
b as

which is our answer.
The ladder reaches
feet up the wall.
Hope that helped! =)