A12-foot ladder rests against the side of a house. the base of the ladder is 3 feet away from the side of the house. how high above the ground is the top of the ladder? round to the nearest tenth of a foot.

Using Pythagorean's Theorem we know that a^2 + b^2 = c^2
C is the length of the ladder, and we are given one of the sides, let's call that side b
                                                                                           
we have a^2 + b^2 = c^2, and a^2 = c^2 - b^2, so a = √ c^2 - b^2
                 
a = √12^2-3^2 = √ 144-9 = √ 135 = 11.61895 
so the top of the ladder is 11.6 feet above the ground

This question is asking about the Pythagorean Theorem (A^2 + B^2 = C^2)

You know the length of the hypotenuse (this is 12 feet, the length of the ladder, which is C), you also know A, 3 feet from the side of the house.

So we have to plug into the formula what we know 3^2 + B^2 = 12^2, or 9 + B^2 = 144. By rearranging the formula you get 144 - 9 = B^2. Once you solve for B^2 you can take the square root to get B. (It's 11.6!)