Question

1. What is the value of x? Do not convert to decimal. Keep your answer in exact (radical) form. Show all of your work. This is Pythagorean theorem, the hypotenuse is the square root of 177, and for the bottom of the triangle it is x, and the back side of the triangle is 8.

Answer 1

The value of x is
`√(113)`.

Explanation:

It is given that hypotenuse is
`√(177)`. So, the legs would be x and 8.

Let's use Pythagoras theorem,

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

Plug in the numbers to solve for x.

`x^(2) +8^(2) =√(177) ^(2)`

Simplify it

`x^(2) +64 =177`

Subtract both sides 64.

`x^(2) =113`

Take square root on both sides

x=
`√(113)`

We can not simplify the radical.

So, let's keep this as answer.