Help me please guys. Find the measure of angle b using the law of sines.
I need to show full work to the teacher

15.04 degrees or answer A is correct.

The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. The formula for it is A=b•sin a/sin b.

You can transform the law of sines formulas to solve some problems of triangulation (solving a triangle). You can use them to find:

The remaining sides of a triangle, knowing two angles and one side.
The third side of a triangle, knowing two sides and one of the non-enclosed angles. In some cases (ambiguous cases) there may be two solutions to the same triangle. If the following conditions are fulfilled, your triangle may be an ambiguous case:
You only know the angle α and sides a and c;
Angle α is acute (α < 90°);
a is shorter than c (a < c);
a is longer than the altitude h from angle β, where h = c * sin(α) (a > c * sin(α)).

I hate useless complicated math lol ;)