A triangle has sides A,B, and C. If the angle between sides A and B is #(pi)/8#, the angle between sides B and C is #pi/6#, and the length of B is 13, what is the area of the triangle?
First of all, let's rewrite in standard notation. It really helps to do these if we always label the triangle consistently.
The triangle has sides
The remaining angle is
The Law of Sines says
Now the area is
I'm tempted to work out an exact answer, because those sines are all expressible using the usual operations including square root. But it's late, and the calculator says
Applying the Law of sines,
Formula for area of " Delta, A_t = (1/2) * a b * sin C#