Question 1124547
<br>
For simplicity, I always draw the figure for this problem in the same orientation:
given angle at the left; unknown side length horizontal.<br>
In this example, then, AB (or c) length 42 is slanted up to the right; side BC (or a) is length 33.<br>
The important number here is the height of the triangle, which from the definition of sine is 42*sin(37) = 25.3 to one decimal place.  Since side a is longer than 25.3 and less than 42, there will be two triangles.<br>
Then the law of sines tells us<br>
sin(C)/42 = sin(A)/33  -->  C = sin^-1(42*sin(37)) = 50 degrees.<br>
In the second triangle angle C is 180-50 = 130 degrees.<br>
Use the fact that the sum of the angles of each triangle is 180 degrees to find the measure of angle B in each triangle.<br>
Use the law of sines with each of those measures of angle B to find the lengths of AC in the two triangles.