SOLUTION: what are the missing side lengths (in simple radical form)? http://prntscr.com/ruwz0z

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Question 1155496: what are the missing side lengths (in simple radical form)?
http://prntscr.com/ruwz0z
Found 3 solutions by MathLover1, Boreal, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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use cos%2860%29 and u=8sqrt%283%29 to find hypothenuse s
cos%2860%29=8sqrt%283%29%2Fs
s=8sqrt%283%29%2Fcos%2860%29
s=8sqrt%283%29%2F%281%2F2%29
s=2%2A8sqrt%283%29
s=16sqrt%283%29
then, using Pythagorean theorem we have
t%5E2=s%5E2-u%5E2
t%5E2=%2816sqrt%283%29%29%5E2-%288sqrt%283%29%29%5E2
t%5E2=256%2A3-64%2A3
t%5E2=192%2A3
t%5E2=576
t=sqrt%28576%29
t=24

Answer by Boreal(15235) About Me  (Show Source):
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It is a 1-2-sqrt(3) triangle
the side given is the short side (1) and is 8 sqrt(3)
the hypotenuse is 16 sqrt(3)
the other leg is 8 sqrt(3)*sqrt(3)=8*3=24.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
what are the missing side lengths (in simple radical form)?
http://prntscr.com/ruwz0z
Shorter leg (opposite smaller acute angle) = 8√3

With this being a 30-60-90 right triangle, the longer leg or 

                                    Also, the hypotenuse, or