#8**+1 **

sin A / a = sin B / b

sin (29.8) / 28.6 = sin B / 35.8

35.8 sin (29.8) / 28.6 = sin B

arcsin (35.8 sin (29.8) / 28.6) = B ≈ 38.5°

So....C = 180 - 29.8 - 39.5 = 110.7°

And

a/sin A = c / sin C

28.6 / sin 29.8 = c / sin 110.7

28.6sin 110.7 / sin 29.8 = = 53.8

So 1st triangle

A = 29.8 B = 38.5 C = 110.7

a = 28.6 b =35.8 c = 53.8

Subtract 38.5 from 180 = 141.5° = B

Add this to A = 171.3 < 180 so we have two triangles

And angle C = 180 - 171.3 = 8.7°

So using the Law of Sines again to find c , we have

a /sin A = c / sin C

28.6 / sin 29.8 = c / sin 8.7

28.6sin 8.7 / sin 29.8 = c = 8.7

So ...in the second triangle

A = 29.8 B = 141.5 C = 8.7

a = 28.6 b = 35.8 c = 8.7

CPhill Apr 12, 2019