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 2, what is the area of the triangle?

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Answer 1 · 2018-02-17T04:02:02

$A_t = (1/2) a b sin C =color(green)( 0.3661$

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$C = pi/6, A = pi/12, b = 2$

$hatB = pi - pi/12 - pi/6 = (3pi)/4$

$a / sin A = b / sin B = c / sin C$

$a = (b * sin A) / sin B = (2 * sin (pi/12)) / sin ((3pi)/4) = 0.7321$

$A_t = (1/2) a b sin C = (1/2) * 0.7321* 2 * sin (pi/6) = 0.3661$

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 2, what is the area of the triangle?