OK, so continuing my scenario where we have points:
L=Landmark
A=Current location #1
B=Current Location #2
H=Home

Originally I had taken a bearing of 332 from A to L, then hiked on a bearing of 33 degrees for 1.5 miles to B. Then I took a bearing of 301 degrees from B to L.

From that information, using the Law of Sines I was able to figure out that the defined triangle is:

Point--Angle--OppSideLength
L--31 degrees--1.5 miles
A--61 degrees--2.55 miles
B--88 degrees--2.91 miles

Now the new stuff using the Law of Cosines:
Suppose I know that the bearing from L to Home is 262 degrees and the distance from L to H is 2.566 miles. My goal is to determine the bearing and distance from B to H in order to return home from current location #2.

First I determine the angle between sides LB and LH:
180 - (360-301) - [180 - (360-262)] = 39 degrees

As mentioned, there isn't enough info to use the Law of Sines. Now I can use the Law of Cosines:

BH = SQRT[ 2.566^2 + 2.55^2 - 2(2.566)(2.55) Cos(39) ]
BH = 1.708 miles

Then I use the Law of Sines to find the other angles:
1.708/Sin(39) = 2.566/Sin(B)

Angle at B = ArcSin[(2.566/1.708)Sin(39)] = 71 degrees

Angle at H = 180 - 39 - 71 = 70 degrees

The bearing from B to H is 33+88+71 - 180 = 12 degrees

So, to get home from B I need to travel on a bearing of 12 degrees for 1.7 miles.

Drawing pictures helps me a lot with this stuff.

Very cool!! Thanks again for making my brain work a bit more than it usually would on a day off.

Ken K.