for the angle can be implied from the law of sines:

We denote further (the equation's right side). There are four possible cases:
#If , no such triangle exists because the side does not reach line . For the same reason a solution does not exist if the angle and .
#If , a unique solution exists: , i.e., the triangle is right-angled.
# If two alternatives are possible.
## If , then (the larger side corresponds to a larger angle). Since