A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(3pi)/8# and the angle between B and C is # (5pi)/12#. What is the area of the triangle?

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Answer 1 · 2017-07-23T08:05:24

The area of the triangle is #=4.57u^2#

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The lengths of the sides are

#a=3#

#b=5#

The angles are

#hatA=5/12pi#

#hatB=3/8pi#

Therefore,

#hatC=pi-(5/12pi+3/8pi)=pi-19/24pi=5/24pi#

The area of the triangle is

#area=1/2ab sin (hatC)#

#=1/2*3*5*sin(5/24pi)#

#=4.57u^2#