Question

How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

Answer 1

The missing side of the right triangle is `sqrt192`

Explanation:

The formula for the Pythagorean Theorem is `a^2 + b^2 = c^2`

You are given a=8 and c=16 so plug those numbers into the formula:

`8^2 + b^2 = 16^2`

`64 + b^2 = 256`

Subtract 64 from both sides

`b^2 = 192`

Square root both sides to get rid of the exponent

`sqrt(b^2) = sqrt192`

`b = sqrt192`

`----------`

To simplify `sqrt192` :

Factor 64 out of 192

`sqrt(64(3))`

Rewrite 64 as `8^2`

`sqrt(8^2 * 3)`

Pull terms out from under the radical

`8sqrt3`

The result can be shown in both exact and decimal forms.

Exact Form:
`8sqrt3`

Decimal Form:
13.856406456 . . .