Find all solutions for a triangle with a = 6, b = 8, and A = 150°

6/sin 150 = 8 / sin B

Step-by-step explanation:

6/sin 150 = 8 / sin B

sin 150 = 1/2 so you cross multiply to get 6 sin B = (1/2) • 8

6 sin B = 4

sin B = 4/6

B = inverse sin (4/6) = 42º or 138º

But both of those add to 150 to go over 180 so there are no solutions.

Back in geometry, you had that the larger angle of a triangle is opposite the longer side, right? You can see that 150º can't be opposite 6 because then the angle opposite 8 would have to be larger than 150º which is impossible for a triangle.