## Length of a Leg of a Right Triangle

About Math To Build On || Contents || On to Naming the Sides || Back to the Hypotenuse || Glossary

### Finding the Length of a Leg

If you know the lengths of the hypotenuse and one leg and need to know the length of the other leg, the formula for the right triangle can again be rearranged to find the answer. The variable that represents the unknown side will need to be on a side of the formula by itself. Since you are naming the sides, the variable can be either a or b.

The formula needed to find an unknown leg when the other sides are known is:

Notice, as indicated under the square root symbol, that you subtract the square of the length of the known leg from the square of the length of the hypotenuse to find the unknown leg.

Remember: The hypotenuse is always the longest side and therefore the largest number. Because of this, the square of the leg is always subtracted from the square of the hypotenuse.
Example: If the length of the hypotenuse is 150 and one of the legs is 90, what is the length of the other leg? Let's say 90 is side b.
Remember: The hypotenuse is always c.
When we put the above numbers into the formula, the calculations look like this.

Third side practice: Find the length of the third side. Convert the numbers with units of measurement to a fraction format. Round the rest of the numbers off to 4 decimal places.

Remember:

```           a           c                a           c

(1)  15          20          (7)   8.375      13.5625
(2)   6 1/2"     10 7/16"    (8)  32.975'     52.25'
(3)  12          18          (9)   4          16
(4)   6'4"        9'5"      (10)  12 7/8"     13"
(5)  88'        100'        (11)   5'         10'
(6)  18"         22"        (12)   1'0 1/4"    2'

```