These are all the same. I don't know why me doing another one for you is doing either of us any good, but here goes.
The first step is to label the triangle. Here we have sides a and c, so we can assume the standard labeling, triangle ABC has vertices A, B and C. The three sides are labeled with a small letter corresponding to their opposite angle. So opposite vertex A is side a, opposite vertex B is side b, opposite vertex C is side c.
Now let's assign the knowns. The angle opposite side c is
C=15 degrees. The remaining side must be
b=2 cm with opposite angle
B=105 degrees.
OK, our unknown is a and we know it's a Law of Sines problem so we need A, the opposite angle. That's easy since the angles in a triangle add to 180 degrees,
A = 180 - B - C = 180 - 105 -15 = 60 degrees
A sixty degree angle! Trig's biggest cliche. Let's go on.
All right, we have all the ingredients to apply the Law of Sines:
I only write the part of the Law of Sines I need. I look at the data I have and I pick the right pair of fractions to equate. Now we solve for our unknown.
Then we substitute in what we know.
We put the whole thing into the calculator and get a long approximation which we round.
Answer: 1.8
This one you should be able to get an exact answer for. But I have no idea how you'd feed that one into these awful computer problem sites everyone seems to be using.
If you care, the exact answer is
Type that in the box.