A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-06-14T06:48:43

The area of the triangle is #=1.3u^2#

The angle between #A# and #B# is

#theta=pi-(5/24pi+1/8pi)=pi-8/24pi=2/3pi#

#sintheta=sin(2/3pi)=sqrt3/2#

The area of the triangle is

#A=1/2A*B*sintheta#

#=1/2*1*3*sin(2/3pi)#

#=1/2*3*sqrt3/2#

#=3/4sqrt3#

#=1.3#