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 16, what is the area of the triangle?

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Answer 1 · 2017-06-30T07:02:50

The area of the triangle is #=32u^2#

The angle between side #A# and #C# is

#=pi-(5/12pi+1/12pi)=6/12pi=1/2pi#

This is a right angle triangle.

#sin(1/2pi)=1#

We apply the sine rule

#16/sin(1/2pi)=A/sin(1/12pi)#

#A=16sin(1/12pi)#

#16/1=C/sin(5/12pi)#

#C=16sin(5/12pi)#

The area of the triangle is

#=1/2ACsin(1/2pi)=1/2*16sin(1/12pi)*16sin(5/12pi)#

#=128*0.25#

#=32#