A 12 foot ladder is resting against a wall. The base of the ladder is 3 feet from the base of the wall. How high up the was will the ladder reach?

Question

You have to make a triangle and use the Pythagorean theorem. 

Answer 1

The Pythagorean theorem states that, in a right triangle, the length of the hypotenuse squared equals the sum of the squares of the other two sides or legs of the triangle.  Algebraically, a²+b²=c².  In your example, the length of the ladder would be the hypotenuse and the distance from the wall would be one of the legs.  So substitute these values into the equation to get: 3²+b²=12² or 9+b²=144 and then subtract 9 from both sides to get b²=135.  Therefore b=√135≈11.62.  If your problem requires an exact answer in its most simplified form, please note that √135=3√15.  Hope this helps you out.