Question 91231
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,-0.2,10),
locate(1,2,c)
)}}}


Since we can see that the triangle has legs of 11 and 10 with a hypotenuse of c, 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+10^2=c^2}}}  Plug in a=11, b=10, and c=c. Now lets solve for c



{{{1 2 1 + 1 0 0 =  c  ^ 2}}} Square each individual term




{{{2 2 1 =  c  ^ 2}}} Combine like terms



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



So c approximates to...

{{{14.8660687473186= c}}}


Which means our answer is

{{{c = 14.8660687473186}}}


which is {{{c = 14.866}}} to the nearest thousandth