This is the question:

Question

In triangle LMN, angle LMN = 42 degrees, LN = 32mm, and LM = 42 mm. Calculate all possible measures of angle MLN to the nearest degree. Use the sine ratio and show your work.

Answer 1

just crank it out. We know that
sin42°/32 = sinN/42
sinN = 0.878
N = 61.43° or 118.57°
That means that angle L is 76.57° or 19.43°
Now use those to find MN