# Given right triangle ABC, with right angle at C, if b = 8 and c = 17, using the Pythagorean Theorem, what is a?

May 17, 2018

A is 15.

#### Explanation:

So let write the Pythagorean Theorem equation out.

${a}^{2} + {b}^{2} = {c}^{2}$

So our value of b is 8 and c is 17. So let plug those number into the equation.

${a}^{2} + {8}^{2} = {17}^{2}$

Now you square the known value which you will get:

${a}^{2} + 64 = 289$

Subtract 64 from both sides and you get:

${a}^{2} = 225$

Square both side:

$\sqrt{{a}^{2}}$=$\sqrt{225}$

When squaring ${a}^{2}$ inside the house, the exponent of 2 cancel out which is just a.

So the final answer is a = 15

So let double check to ensure that it adds up to 289. If it does not, then somewhere along the way I made a math calculation error.

${15}^{2} + {8}^{2} = {c}^{2}$
$225 + 64 = {c}^{2}$
$289 = {c}^{2}$
$\sqrt{289} =$sqrt(c^2)#

$17$=$c$

So a = 15 work.