The Ambiguous Case
Key Questions

Answer:
As listed below.
Explanation:
For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). ... If angle A is acute, and a = h, one possible triangle exists

If angle A is acute, and a < h, no such triangle exists.

If angle A is acute, and a = h, one possible triangle exists.

If angle A is acute, and a > b, one possible triangle exists.

If angle A is acute, and h < a < b, two possible triangles exist.

If angle A is obtuse, and a < b or a = b, no such triangle exists.

If angle A is obtuse, and a > b, one such triangle exists.


Three numbers (
#a,b,c# ) can be the lenght of three sides of a triangle if and only if each of them is greater then the difference of the other two, and less of the sum of the other two.I.E: (if
#a>b>c# )#a>bc# ,
#b>ac# ,
#c>ab# ;and:
#a<b+c# ,
#b<a+c# ,
#c<a+b# . 
Answer:
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:

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.


To solve a triangle it is necessary to know at least three elements with an only exception: if these three elements are the three angles.
In fact if two triangles have identical the three angles, they are similar.