Two sides of a triangle are twelve feet, what is the length of the third side?

Since we are only given two congruent sides, we cannot specify the length the third side. However we can describe what it must be... 

First off, our triangle must be isosceles and so the base angles must be congruent. Let's call the unknown side u and the angle between the congruent legs x, then the base angles must be: 

 

and so 

 
Next we can use the Law of Sines to find u 

 

but 
 

so we can write 



 


:)