A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 12, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

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Answer 1 · 2017-06-14T06:41:46

The area of the triangle is #=42u^2#

The angle between #A# and #B# is

#theta=pi-(11/24pi+1/24pi)=pi-12/24pi=1/2pi#

#sintheta=sin(1/2pi)=1#

The area of the triangle is

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

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

#=42#