Question

Given the sample triangle below and the conditions sin B = 1/2, a= 20 , find te hypotenuse of triangle

Answer 1

Draw a triangle with horizontal base and hypotenuse rising from lower left to upper right at a 30 deg. angle. 
The side labelled a =20 can't be the hypotenuse otherwise why ask to find the hypotenuse? It can't be the 
vertical side because, for sin = 1/2, vertical = (1/2)hypotenuse and hypotenuse = (2)vertical = 40. This 
would trivialize the problem so the only side to be labelled a = 20 is the horizontal base. So we label the 
vertical side t and the hypotenuse 2t. Then we have (2t)^2 = t^2 + (20)^2, ie., 3t^2 = (20)^2, t = 20/rt3, and 
2t

ANSWER:hypotenuse = (40/3)rt3.