Question

How many solutions does a triangle with values a = 42, A = 117 degrees, and b = 34 have

Answer 1

let's use the sine law ...

sin B/34 = sin 117°/42
sin B = 34sin117/42 = .72129...
B = 46.2° or by the CAST rule B could be 133.8°
But, that would mean the angle has 2 obtuse angle, which is not possible

so angle B = 46.2° and there is only one triangle possible
One set of solutions.

Answer 2

zero solutions

Answer 3

There is actually one solution