The Pythagorean Theorem Examples

A right triangle has one leg of length 5 and a hypotenuse of length 16. What is the length of the other leg of the triangle?

Draw a picture to help us visualize:

We need to find a, the length of the remaining leg. Time's a-wastin', so shake a leg.

The Pythagorean Theorem tells us that a² + 5² = 16², or a² + 25 = 256.

Then a² = 231, so .

Since a is a length, the final answer is .

A right triangle has a hypotenuse of 30 inches. Both of its legs are the same length. How long is a leg of this right triangle?

This problem is describing a triangle that looks like this:

We know that if we sum the squares of the legs, we find the square of the hypotenuse. We said that earlier, in that sentence you reread 37 times. Therefore:

x² + x² = 30²

Or:

2x² = 900

From this point onward, it's kid's stuff. We divide each side by 2 to find x² = 450:

Since we're talking about a triangle here, we can't have a side with a negative length. As screwy as our system of measurement is compared to the metric system, at least there's no such thing as negative inches, even if a British person (hi, guys!) tries to imply that there is.

We determine that a leg of this triangle must have length .