How do you find the second triangle in the ambiguous case?
As listed below.
If the sum is over 180°, then the second angle is not valid. First we know that this triangle is a candidate for the ambiguous case since we are given two sides and an angle not in between them. We need to find the measure of angle B using the Law of Sines: If their sum is less than 180°, we know a triangle can exist.
To determine if there is a 2nd valid angle:
See if you are given two sides and the angle not in between (SSA). This is the situation that may have 2 possible answers.
Find the value of the unknown angle.
Once you find the value of your angle, subtract it from 180° to find the possible second angle.
Add the new angle to the original angle. If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid.
If already one obtuse angle given, it can not have a second set of values.