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#### The Pythagorean Theorem

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#### Knowledge

If c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation:

a^{2} + b^{2} = c^{2}

If the lengths of both a and b are known, then c can be calculated as

c = a^{2} + b^{2}

If the length of the hypotenuse c and of one side (a or b) are known, then the length of the other side can be calculated as

a = c^{2} - b^{2}
or
b = c^{2} - a^{2}

#### Example 1

Find the value of ? in the triangle shown below.

4^{2} + 3^{2} = ?^{2}

16 + 9 = ?^{2}

25 = ?^{2}

25 = ?^{2}

5 = ?^{2}

#### Example 2

Find the value of ? in the triangle shown below.

9^{2} - 8^{2} = ?^{2}

81 - 64 = ?^{2}

17 = ?^{2}

17 = ?^{2}