A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 8, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

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Answer 1 · 2016-06-29T18:28:00

Area of #DeltaABC=38.636# sq. unit.

Let us denote by #/_(A,C)# the angle btwn. sides #A & C.#

Then, by what is given, we find, #/_ (A,C)+/_ (B,C)=(13pi)/24+pi/24=(14pi)/24=(7pi)/12.#

Hence, #/_ (A,B)=pi-(7pi)/12=(5pi)/12.#

Now by Formula from Trigo.,
Area of #DeltaABC=1/2*A*B*sin/_ (A,B)=1/2*10*8*sin((5pi)/12)=40*sin75^o=40(0.9659)=38.636# sq. unit.