A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12 and the angle between sides B and C is pi/12. If side B has a length of 4, what is the area of the triangle?

1 Answer
Feb 27, 2016

pl,see below

Explanation:

The angle between sides A and B =5pi/12
The angle between sides C and B =pi/12
The angle between sides C and A =pi -5pi/12-pi/12=pi/2
hence the triangle is right angled one and B is its hypotenuse.
Therefore side A = Bsin(pi/12)=4sin(pi/12)
side C = Bcos(pi/12)=4cos(pi/12)
So area = 1/2ACsin(pi/2)=1/2*4sin(pi/12)*4cos(pi/12)
=4*2sin(pi/12)*cos(pi/12)
=4*sin(2pi/12)
=4*sin(pi/6)
=4*1/2 =2 sq unit