Question

How do you find the second triangle in the ambiguous case?

Answer 1

As listed below.

Explanation:

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.

(http://www.softschools.com/math/calculus/the_ambiguous_case_of_the_law_of_sines/)

To determine if there is a 2nd valid angle:

1. See if you are given two sides and the angle not in between (SSA). This is the situation that may have 2 possible answers.

2. Find the value of the unknown angle.

3. Once you find the value of your angle, subtract it from 180° to find the possible second angle.

4. 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.

5. If already one obtuse angle given, it can not have a second set of values.