# A right triangle's leg is 9 and the hypotenuse is 15, what is the other leg s length?

##### 2 Answers

The length of the other leg is 12

#### Explanation:

The Pythagorean theorem is:

Where "a" and "b" legs of the triangle and side "c" is the hypotenuse.

We are given that the triangles right leg is 9 and the hypotenuse is 51. Because addition is commutative, it does not matter whether we choose to assign "a" or "b" the known length; I shall choose "a":

Let

Substitute this into equation [1]:

Compute the squares:

Subtract 81 from both sides:

Square root both sides:

Discard the negative length:

The length of the other leg is 12

The second leg's length is

#### Explanation:

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem,

If one leg is

If the hypotenuse is

Now we just have to find the

Plugging in the variables,