Answer:
The value of x is [tex]\sqrt{113}[/tex].
Step-by-step explanation:
It is given that hypotenuse is [tex]\sqrt{177}[/tex]. So, the legs would be x and 8.
Let's use Pythagoras theorem,
[tex]a^{2} +b^{2} =c^{2}[/tex]
Plug in the numbers to solve for x.
[tex]x^{2} +8^{2} =\sqrt{177} ^{2}[/tex]
Simplify it
[tex]x^{2} +64 =177[/tex]
Subtract both sides 64.
[tex]x^{2} =113[/tex]
Take square root on both sides
x=[tex]\sqrt{113}[/tex]
We can not simplify the radical.
So, let's keep this as answer.
