A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 35, what is the area of the triangle?

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Answer 1 · 2018-04-07T10:20:32

$color(blue)("Area of " Delta " " A_t = 129.44$

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

![https://math.stackexchange.com/questions/811938/law-of-sines-and-cosines]( useruploads.socratic.org )

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

$a = (35 * sin (pi/12)) / sin ((2pi)/3) = 10.46$

$color(green)("Area of Triangle " A_t = (1/2) a b sin C$

$A_t = (1/2) * 10.46 * 35 * sin(pi/4) = 129.44$

A triangle has sides A, B, and C. The angle between sides A and B is pi/4π4pi/4 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 35, what is the area of the triangle?