A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-07-17T17:14:51

The area is #=9.66u^2#

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The dimensions of the triangle are

Side #a=4#

Side #b=5#

Angle #hatB=5/24pi#

Angle #hatA=3/8pi#

Therefore,

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

#=pi-7/12pi#

#=5/12pi#

The area of the triangle is

#=1/2*a*b*sin hatC#

#=1/2*4*5*sin(5/12pi)#

#=9.66u^2#