Question

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

Answer 1

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.

Answer 2

`a = sqrt39`

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 = sqrt39`

Answer 3

If you are finding the hypotenuse

`5^2+8^2=a^2`

`25+64=a^2`

`a=sqrt89`

a=9.433981132

If `c` is the hypotenuse then

`8^2-5^2=a^2`

`64-25=a^2`

`a=sqrt39`

a=6.244997998