Answer: The way to work this problem is to sketch the SSA-described triangle.
Horizontally, mark a ray stemming from point C, going to the right.
From point C, at an angle of elevation of 20 degrees, draw a segment a = 6.3, ending at point B.
Now, from point B, draw a segment perpendicular to the horizontal ray and label it h, for altitude.
Calculate h = 6.3 sin 20o = 2.1547.
Now imagine that, dangling from point B, you have a segment of length c = 9.3; in fact, put a compass with steel point at B and radius 9.3, and draw a big arc. you'll see that it can intersect the horizontal ray only once; in its swing toward point C, due to c > a, there will be no second intersection of the ray (the arc 'overshoots' the ray).
Thus you see that only one solution exists, and the Law of Sines can be used to solve the triangle:
sin 20 / 9.3 = sin A / 6.3 and this leads to A = 13.4 degrees...and B = 180 - 20 - 13.4 = 146o.
I'll let you solve for b (side AC).
