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 $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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.

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)/2413π24(13pi)/24 and the angle between B and C is (pi)/24π24 (pi)/24. What is the area of the triangle?