A triangle has sides A, B, and C. The angle between sides A and B is $pi/4$ and the angle between sides B and C is $pi/12$ . If side B has a length of 10, what is the area of the triangle?

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Answer 1 · 2018-03-27T02:29:32

$color(brown)(A_t = (1/2) * a * b * sin C = 10.6 " sq units"$

$hat A = pi/12, hat C = pi/4, b = 10$

$hat B = pi - pi/12 - pi/4 = (2pi)/3$

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

$a = (b * sin A ) / sin B = (10 * sin (pi/12)) / sin ((2pi)/3) ~~ 3 " units"$

$"Area of the triangle " A_t = (1/2) * a * b * sin C$

$color(brown)(A_t = (1/2) * 3 * 10 * sin (pi/4) = 10.6 " sq units"$

A triangle has sides A, B, and C. The angle between sides A and B is pi/4pi/4 and the angle between sides B and C is pi/12pi/12. If side B has a length of 10, what is the area of the triangle?