solve any triangles satisfying

alpha = 20 degrees
b = 10
c = 16

b and c are 2 side values and if I use the pythagorean theorem and I get 18.18? Did I do this right?

You had a similar question yesterday.

I answered it but it appears you didn't look at.
It does not state that it is a right-angled triangle, assuming it is results in contradictory results.

http://www.jiskha.com/display.cgi?id=1352817903