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

Mar 31, 2017

The length of the other leg is 12

#### Explanation:

The Pythagorean theorem is:

${a}^{2} + {b}^{2} = {c}^{2} \text{ [1]}$

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 $a = 9$ and $c = 15$

Substitute this into equation [1]:

${9}^{2} + {b}^{2} = {15}^{2}$

Compute the squares:

$81 + {b}^{2} = 225$

Subtract 81 from both sides:

${b}^{2} = 144$

Square root both sides:

$b = \pm 12$

$b = 12$

The length of the other leg is 12

Mar 31, 2017

The second leg's length is $12$.

#### Explanation:

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem, ${a}^{2} + {b}^{2} = {c}^{2}$.

If one leg is $9$, that's our $a$ value.
If the hypotenuse is $15$, that's our $c$ value.
Now we just have to find the $b$ value.

Plugging in the variables, ${9}^{2} + {b}^{2} = {15}^{2}$.

${9}^{2} = 81$.
${15}^{2} = 225$.

$81 + {b}^{2} = 225$. Subtract $81$ from both sides.

${b}^{2} = 144$. Square root both sides.

$\sqrt{{b}^{2}} = b$ and $\sqrt{144} = 12$, so $b = 12$