How high does the ladder touch?

A 12 foot ladder is three and a half feet from a wall. How high on the wall does the ladder touch?

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A right triangle is formed, with one leg being 3.5 and the hypotenuse being 12.

Pythagorean Theorem
a² + b² = c²   {the sum of the squares of the legs is equal to the square of the hypotenuse}
a and b are the legs
c is the hypotenuse {the side across from the right angle}

3.5² + b² = 12²   {substituted into the Pythagorean Theorem}
12.25 + b² = 144   {evaluated exponents}
b² = 131.75   {subtracted 12.25 from each side}
b ≈ 11.48   {took square root of each side and rounded}

The ladder touches approximately 11.48 feet up the wall.

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