1. ## Ambiguous Case (SSA)

What does h represent? side c???

Thanks a bunch

2. ## Re: Ambiguous Case (SSA)

Originally Posted by Ashz

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: $\angle A < 90 \text{ and } h = b \sin A$

If $a >= b$, we have only one solution

If $a < b$, then we need to compare a with h.

If $a, then there is no solution.
If $a=h$, then there is one solution.
If $a>h$, then there are two solutions.

II. Case 2: $\angle A > 90$

If $a \le b$, then there is no solution.

If $a>b$, 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.

3. ## Re: Ambiguous Case (SSA)

HAHAHA I think I <3 you! Thanks