A triangle has sides A, B, and C. If the angle between sides A and B is $(pi)/12$ , the angle between sides B and C is $(5pi)/12$ , and the length of B is 10, what is the area of the triangle?

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Answer 1 · 2017-08-17T12:13:29

The area of the triangle is $12.50$ sq.unit .

The angle between sides $A and B$ is $/_c = pi/12=180/12= 15^0$

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

The angle between sides $C and A$ is $/_b = 180-(75+15)=90^0$

We can find side $A$ by aplying sine law $A/sina = B/sinb ; B=10$

$A = B* sina/sinb = 10 * sin 75/sin90 ~~ 9.66$

Now we have Sides $A(9.66) , B(10)$ and their included angle

$/_c = 15^0$ . The area of the triangle is $A_t= (A*B*sinc) /2$

or $A_t= (10*9.66*sin 15)/2 = 12.50$ sq.unit [Ans]

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/12(pi)/12, the angle between sides B and C is (5pi)/12(5pi)/12, and the length of B is 10, what is the area of the triangle?