difficult precalc problems that i just dont understand

1. In triangle ABC, angle BCA = pi/6, AB = 4 and AC = 10. 

 

2. In triangle ABC, angle BCA = pi/6, AB = 5 and AC = 10. 

 

3. In triangle ABC, angle BCA = pi/6, AB = 6 and AC = 10. 

 

GOAL: Find the sum of all distinct possible values of BC. IF THERE ARE NO VALUES, just put no values.

 

I spent an hour on these, it would be nice to recieve some help.