A triangle has sides A, B, and C. The angle between sides A and B is #pi/4# and the angle between sides B and C is #pi/12#. If side B has a length of 17, what is the area of the triangle?
First find the third angle, between sides A and C:
Now, Use the Law of Sines to find a second side. We choose side A and must know the sine of
And then the Law of Sines gives:
Now that we have two sides A and B, we can take half their product time the sine of the included angle: