A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 14, what is the area of the triangle?

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Answer 1 · 2018-02-17T09:28:51

Area of $Delta ABC = (1/2) a b sin C = color(green)(17.9352$

$hatA = pi/12, C = pi/6, b = 14$

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

$a / sin A = b / sin B$

$a = (14 * sin (pi/12)) / sin ((3pi)/4) = 5.1244$

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Area of $Delta ABC = (1/2) a b sin C = 0.5 * 5.1244 * 14 * sin (pi/6) = color(green)(17.9352$

A triangle has sides A, B, and C. The angle between sides A and B is pi/6π6pi/6 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 14, what is the area of the triangle?