Question

A triangle has sides A, B, and C. The angle between sides A and B is #pi/6# and the angle between sides B and C is #pi/12#. If side B has a length of 5, what is the area of the triangle?

Answer 1

Use the Law of Sines to solve for side c. Then you can you the two sides (c and b) and their included angle to find the area using.
sin(pi/6)/c = pi/12/5   cross multiply and divide 5*sin(pi/6)/pi/12 = 9.5
That makes side c= 9.5.
now use the formula for finding area with two sides and their included angle. It must the angle between them.
(1/2)(9.5)(5)cos(pi/12) multiply that all together and you should get the area equals 22.9