Question 14981
In my very last solution that I posted not 5 minutes ago, this same concept came up.  This is a right triangle whose hypotenuse is the 5 foot ladder.  It reaches the wall 3 feet from the wall, which is the first leg, and the second leg is the unknown x, which is the distance up the wall where the ladder reaches at the top.


{{{x^2 + 3^2 = 5^2}}}


If you are familiar with the special right triangle whose sides are 3, 4, 5, or any multiple thereof, then you recognize that the unknown side is 4 feet.  


If you are NOT familiar with these special triangles, then you solve the equation 
{{{x^2 + 3^2 = 5^2}}}
{{{x^2 + 9 = 25}}}
{{{x^2 = 16}}}
x=4 feet.


Either way, the unknown side of the right triangle is 4 feet (up the wall!).


R^2 at SCC