Question 104465
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(-0.2,1.5,12),
locate(1,-0.2,x),
locate(1,2,24)
)}}}

Since we can see that the triangle has legs of 12 and x with a hypotenuse of 24, 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




{{{12^2+x^2=24^2}}}  Plug in a=12, b=x, and c=24. Now lets solve for x



{{{1 4 4 +  x  ^ 2 = 5 7 6}}} Square each individual term




{{{ x  ^ 2 = 5 7 6 - 1 4 4}}} Subtract 144 from both sides



{{{ x  ^ 2 = 4 3 2}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 4 3 2 )}}} Take the square root of both sides



{{{x=12*sqrt(3)}}} Simplify the square root



Which approximates to...

{{{x = 2 0 . 7 8 4 6 0 9 6 9 0 8 2 6 5}}}


So our answer is

{{{x = 2 0 . 8}}}