# How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: b = 5, c = 8?

May 14, 2018

Side A is $\sqrt{39}$ or 6.244997998.

#### Explanation:

Right, let write down the Pythagorean Theorem equation or standard form of it. before we plug in the numbers.

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

Right, so that is the equation of Pythagorean Theorem. So let plug in the numbers of b and c.

${a}^{2} + {5}^{2} = {8}^{2}$

So we have our values of b and c. Now, how do we find the missing number?

Well, let simplify thing further by squaring the numbers we have already.

${a}^{2}$ + 25 = 64

We will now subtract 25 from both side which gives us:

${a}^{2}$ = 39

Now we can square root the answer.

$\sqrt{{a}^{2}}$ = $\sqrt{39}$

Now, we are left with this:
a = $\sqrt{39}$

Now, I am unsure if you want decimals or not. But if you were to square 39 into your calculator by pressing a few keys, it would give you this unless you switched mode.

On my calculator model of TI-36XPro, I pressed "mode" and went to the bottom and switched from Hathprint to Classic which gives me decimals of square roots.

So the final answer is $\sqrt{39}$ or the decimal value of $\sqrt{39}$ is 6.244997998.

May 14, 2018

$a = \sqrt{39}$

#### Explanation:

The Pythagorean Theorem is ${a}^{2} + {b}^{2} = {c}^{2}$

You can then substitute the numbers b and c to get:
${a}^{2} + {5}^{2} = {8}^{2}$
${a}^{2} + 25 = 64$

You can then make ${a}^{2}$ on its own by $- 25$
${a}^{2} = 39$

Then square root both sides to get:
$a = \sqrt{39}$

May 14, 2018

If you are finding the hypotenuse

${5}^{2} + {8}^{2} = {a}^{2}$

$25 + 64 = {a}^{2}$

$a = \sqrt{89}$

a=9.433981132

If $c$ is the hypotenuse then

${8}^{2} - {5}^{2} = {a}^{2}$

$64 - 25 = {a}^{2}$

$a = \sqrt{39}$

a=6.244997998