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 $pi/6$ . If side B has a length of 8, what is the area of the triangle?

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Answer 1 · 2018-03-27T03:03:20

$color(green)(Delta " " A_t = (1/2) a b sin C = 11.71 " sq units"$

$hat A = pi/6, hat C = pi/4, b = 8$

$hat B = pi - pi/6 - pi/4 = (7pi)/12$

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

$a = (b sin A) / sin B = (8 * sin (pi/6) ) / sin ((7pi)/12) = 4.14 " units"$

$color(green)(Delta " " A_t = (1/2) a b sin C = (1/2) * 4.14 * 8 * sin (pi/4) = 11.71 " sq units"$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4(pi)/4 and the angle between sides B and C is pi/6pi/6. If side B has a length of 8, what is the area of the triangle?