Question 115195
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(-0.2,1.5,11),
locate(1,-0.2,x),
locate(1,2,16)
)}}}

Since we can see that the triangle has legs of 11 and x with a hypotenuse of 16, 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




{{{11^2+x^2=16^2}}}  Plug in a=11, b=x, and c=16. Now lets solve for x



{{{1 2 1 +  x  ^ 2 = 2 5 6}}} Square each individual term




{{{ x  ^ 2 = 2 5 6 - 1 2 1}}} Subtract 121 from both sides



{{{ x  ^ 2 = 1 3 5}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 1 3 5 )}}} Take the square root of both sides



{{{x=3*sqrt(15)}}} Simplify the square root



Which approximates to...

{{{x = 1 1 . 6 1 8 9 5 0 0 3 8 6 2 2 3}}}


So our answer is

{{{x = 1 1 . 6 1 8 9 5 0 0 3 8 6 2 2 3}}}