Question 109598
We basically have this triangle set up:


{{{drawing(500,500,-3,1,-0.5,3.3,

line(0,3,-2,0),
line(-2,0,0,0),
line(0,0,0,3),
locate(0.2,1.5,8),
locate(-1,-0.05,5),
locate(-1,2,x)
)}}}

Since we can see that the triangle has legs of 5 and 8 with a hypotenuse of x, 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




{{{5^2+8^2=x^2}}}  Plug in a=5, b=8, and c=x. Now lets solve for x



{{{2 5 + 6 4 =  x  ^ 2}}} Square each individual term




{{{8 9 =  x  ^ 2}}} Combine like terms



{{{s q r t ( 8 9 ) = s q r t (  x  ^ 2 )}}} Take the square root of both sides


{{{x=sqrt(89)}}} Simplify



Which approximates to...


{{{x=9.4339811320566}}}


So our answer is

{{{x=9.4339811320566}}}