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

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Answer 1 · 2017-08-07T12:06:42

Area of the triangle is $0.09$ sq. unit.

The angle between sides $A and B$ is $/_c= pi/6=180/6= 30^0$ .

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

The angle between sides $C and A$ is $/_b= 180-(30+15)=135^0$

$B=1$ . Applying sine law we get $A/sina = B/sinb$

$:. A = B * (sina/sinb) = 1 * sin15/sin135 =0.366$

Now we have $A = 0.366 , B =1$ and their icluded angle

$c=30^0$ :. Area of the triangle is $A_t = (A*B*sinc)/2$ or

$A_t= (1*0.366*sin30)/2 = (0.366 * 1/2)/2 ~~ 0.09$ sq. unit Ans]

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