To explain the method, let's use a triangle with a side length of 9 and two adjacent angles of 40 and 45 degrees. The first step is to square 9 and divide by 2. So (9)(9) = 81 and 81/2 = 40.5.
The next step in calculating the area is to take the number you found in step one and multiply it by the sines of 40 degrees and 45 degrees. Sine(40) = .6428, and sine(45) = .7071. And so (40.5)(.6428)(.7071) = 18.4082.
Next, use a calculator or trig table to find sine(40+45) = sine(85) = .9962. Now divide the number you got in step 2 by sine(85). 18.4082/.9962 = about 18.5. So the area of the triangle is 18.5 square units.
If you have a side length of A and two adjacent angles of x and y degrees, the general formula for the area of a triangle is [(1/2)A²sine(x)sine(y)]/sine(x+y).