A12 foot ladder leans against the side of a house the bottom of the ladder is 7 ft from the side of the house how high is the top of the ladder from the ground

he 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.

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