Since the side opposite the given angle is shorter than
the other given side, there are either 2 or 0 solutions.
[If there were 0 solution we will encounter an error
in the calculator, or observe that a sine cannot be 
greater than 1.]

Using the law of sines:



Cross-multiply:



Substitute given quantities



Divide both sides by 15.8



Calculate the right side on your calculator:



Use the inverse sine feature on your calculator:

You get 52.70708059°, but that is only the possible
angle in QI where angles are acute (less than 90°).  
But the sine is also positive in QII where angles 
are obtuse (greater than 90° but less than 180°).

So the two possible angles for N are 1)  52.70708059°
and 2)  its supplement 180°-52.70708059° = 127.2929194°.

Solving the first triangle which has parts:

L=42.8° , l = 15.8cm , n=18.5cm, N=52.70708059°

And since the sum of the angles of any triangle is 180°,

M = 180°-(L+N) = 180°-(42.8°+52.70708059°) = 84.49291941°

We use the law of sines:



Multiply both sides by sin(M)



Substitute known parts:



Use your calculator



So the first solution is

L=42.8° , l=15.8cm , n=18.5cm, 
N=52.70708059°, M=84.49291941°, m=12.62795038cm

Now you can solve the second triangle which has parts:

L=42.8° , l = 15.8cm , n=18.5cm, N=127.2929194° 

exactly as I solved the first triangle, only using 
N=127.2929194° instead.

Edwin