A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/12$ and the angle between sides B and C is $pi/6$ . If side B has a length of 1, what is the area of the triangle?

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Answer 1 · 2016-11-14T12:17:51

The area of the triangle is $1/4 sq.unit$

The angle between sides $A and B$ is $/_c=(5pi)/12=(5*180)/12=75^0$ .

The angle between sides $B and C$ is $/_a=pi/6=180/6=30^0$

The angle between sides $A and C$ is $/_b=180-(75+30)=75^0$

$/_b= /_c=75^0$ . So it is an isocelles triangle , having opposite sides equal. So $B=C=1$ and their included angle $/_a=30^0$

Hence the area of the triangle is $A_t=(B*C*sin a)/2=(1*1*sin30)/2=1/4 sq.unit$ [Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12(5pi)/12 and the angle between sides B and C is pi/6pi/6. If side B has a length of 1, what is the area of the triangle?