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 12, what is the area of the triangle?

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Answer 1 · 2016-02-28T19:30:43

Angle C is $pi/6$ and angle A is $pi/12$ . Hence angle B= $pi-pi/6-pi/12= (3pi)/4$

Side b =12 , therefore using the formula $sinA/a= SinB/b$

it would be side a= b sinA/ SinB= $12 sin (pi/12)/sin((3pi)/4)$

For area of triangle use the formula $1/2 ab sinC$

= $(1/2)12(12) sin (pi/12)/sin((3pi)/4) sin (pi/6)$

= $72(0.2588)(0.5)/0.7071$

=13.176

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 12, what is the area of the triangle?