Question 143529
We basically have this triangle set up:


{{{drawing(500,500,-0.5,2,-0.5,3.2,

line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,2),
locate(1,-0.2,x),
locate(1,2,8)
)}}}

Since we can see that the triangle has legs of 2 and x with a hypotenuse of 8, we can use Pythagoreans theorem to find the unknown side.



Pythagoreans theorem:


{{{a^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse




{{{2^2+x^2=8^2}}}  Plug in a=2, b=x, and c=8. Now lets solve for x



{{{4 +  x  ^ 2 = 6 4}}} Square each individual term




{{{ x  ^ 2 = 6 4 - 4}}} Subtract 4 from both sides



{{{ x  ^ 2 = 6 0}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 6 0 )}}} Take the square root of both sides



{{{x=2*sqrt(15)}}} Simplify the square root




So you are correct