Finding the Hypotenuse with the Pythagorean Theorem

0:00A right triangle has one right angle, an angle of 90 degrees.

0:05The two sides that form the right angle are the legs: here, 6 metres and 8 metres.

0:12The side opposite the right angle is the hypotenuse, the longest side. How long is it?

0:19Call the legs a and b, and the hypotenuse c. The Pythagorean theorem says c squared equals a squared plus b squared.

0:30Here a is 6 and b is 8, so c squared equals 6 squared plus 8 squared.

0:37Squaring means multiplying a number by itself. 6 times 6 is 36, and 8 times 8 is 64.

0:47Add: 36 plus 64 is 100, so c squared is 100.

0:54To undo the squaring, take the square root. The square root of 100 is 10, because 10 times 10 is 100.

1:03So the hypotenuse is 10 metres, longer than each leg, as it should be.

1:09A common mistake is adding the legs: 6 plus 8 is 14. But the legs together are always longer than the hypotenuse.

1:19Another mistake is forgetting the square root. c squared is 100, but c is 10 metres.

1:27Now a second triangle, with legs of 5 centimetres and 7 centimetres.

1:33c squared is 5 squared plus 7 squared. That is 25 plus 49, which makes 74.

1:41No whole number times itself makes 74, so a calculator gives the square root: about 8.6 centimetres. The wavy sign means approximately equal.

1:54Check: 8.6 times 8.6 is 73.96, very close to 74.

2:02To find the hypotenuse, square both legs, add them, then take the square root.