Please see attachment
What does h represent? side c???
Thanks a bunch
Hi Ashz,
h is the height of the triangle.
Let me state the ambiguous case a little differently. You might reference: The law of sines, including the ambiguous case.
Consider triangle ABC, with sides a, b, c (a opposite angle A, b opposite angle B, and c opposite angle C)
I. Case 1: $\displaystyle \angle A < 90 \text{ and } h = b \sin A$
If $\displaystyle a >= b$, we have only one solution
If $\displaystyle a < b$, then we need to compare a with h.
If $\displaystyle a<h$, then there is no solution.
If $\displaystyle a=h$, then there is one solution.
If $\displaystyle a>h$, then there are two solutions.
II. Case 2: $\displaystyle \angle A > 90$
If $\displaystyle a \le b$, then there is no solution.
If $\displaystyle a>b$, then there is one solution.
I hope this helps. It sounds like a lot of stuff to keep up with, but keep the notes handy and it will take the mystery out of the ambiguous case.
I like to call this case the "Donkey Law of Sines" because it comes into play only when you have an Angle - Side - Side situation or "ASS". Politically correct texts call it SSA.