A triangle has sides A, B, and C. The angle between sides A and B is #pi/3# 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?

1 Answer
May 19, 2016

Area of triangle is #2.90#

Explanation:

The third angle opposite sides #A# and #C# is

#pi-pi/3-pi/12=(12-4-1)pi/12=5pi/12# and it has side #B=5# opposite it.

As side #A# has angle opposite it #pi/12#, using sine formula, we get

#A/sin(pi/12)=B/sin((5pi)/12)# or

#A=Bxxsin(pi/12)/sin((5pi)/12)=5xx0.2588/0.9659=1.34#

Hence area of triangle is #1/2xx5xx1.34xxsin(pi/3)#

= #1/2xx5xx1.34xx0.866=2.90#