A triangle has sides A,B, and C. If the angle between sides A and B is #(7pi)/12#, the angle between sides B and C is #pi/4#, and the length of B is 7, what is the area of the triangle?

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Answer 1 · 2017-06-19T10:01:35

The area of the triangle is #=33.5u^2#

The angle between #A# and #C# is

#=pi-(7/12pi+1/4pi)#

#=pi-10/12pi#

#=2/12pi=1/6pi#

#B=7#

We apply the sine rule

#A/sin(1/4pi)=B/sin(1/6pi)#

#A=(Bsin(1/4pi))/sin(1/6pi)#

The area of the triangle is

#=1/2*A*B*sin(7/12pi)#

#=1/2*B*(Bsin(1/4pi))/sin(1/6pi)*sin(7/12pi)#

#=1/2*B^2*(sin(1/4pi))/sin(1/6pi)*sin(7/12pi)#

#=1/2*49*1.366#

#=33.5#