Martín’s house has a window with a ledge that is four feet off the ground, and he grows flowers on this ledge. Martín is much too busy to take care of the flowers, so he hired a magic little elf to water the flowers for him. The elf is very, very small and cannot reach the flowers on his own. Martín left a five-foot tall ladder out for the elf to use. How far would the magic elf have to place the ladder from the house in order to reach the window ledge?

Here, you can imagine a right-angled triangle. The two legs being the wall and the ground, and the ladder is the hypotenuse. Since we are given the hypotenuse, and one of the legs, we can solve the Pythagorean's Theorem for one side:
[tex]a^2+b^2=c^2[/tex]
[tex]b = \sqrt{c^2-a^2} [/tex]

Plug in known values (remember, c is the hypotenuse, INC the ladder):
[tex]b = \sqrt{5^2-4^2} = \sqrt{25-16} = \sqrt{9} =3, -3[/tex]

Since we only care about the positive distance, the answer cannot be negative.So, the tiny, tiny elf would have to put the ladder 3ft away from the wall! Hope this is helpful! If you need anymore help, feel free to drop a message!