Question

Find the length of the third side, if necessary, write in simplest radical form.

Answer 1

The length of the third side is 7.

Explanation:

We can use the Pythagorean theorem to evaluate the length of the third side.

`a^2+b^2=c^2`

Let the third side be
`a`.

Lets solve for
`a.`

Subtract
`b^2` from both sides.

`a^2=c^2-b^2`

Take the square root of both sides.

`a=√(c^2-b^2)`

We are given

`c=√(58) \\b=3`

Lets evaluate
`a`.

`a=\sqrt{(√(58) )^2-3^2}`

Simplify.

`a=√(58-9)\\a=√(49) \\a=7`