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Pythagorean Theorem

The Pythagorean theorem is a tool that can be used to solve for unknown values on right triangles. In order to use the Pythagorean theorem, a term must be defined. The term hypotenuse is used to describe the side of a right triangle opposite the right angle. Line segment C is the hypotenuse of the triangle in the diagram below. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

This may be written as c2 = a2+ b2,or c = √a2+b2

Example:

The two legs of a right triangle are 5 ft and 12 ft. How long is the hypotenuse?

Solution

Let the hypotenuse be c ft.

c2 = a2+ b2

c2 = 122 + 52

c2 = 144 + 25

c2 = 169

c = √169

c = 13 feet

Using the Pythagorean theorem, one can determine the value of the unknown side of a right triangle when given the value of the other two sides.

Example:

Given that the hypotenuse of a right triangle is 18" and the length of one side is 11", what is the length of the other side?

Solution

c2 = a2+ b2

112+ b2 = 182

b2 = 182 - 112

b2 = 324 - 121

b2 = 203

b = √203

b = 14.2 in.

Pythagorean Theorem Summary:

The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

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