A triangle has sides A,B, and C. If the angle between sides A and B is $(3pi)/4$ , the angle between sides B and C is $pi/6$ , and the length of B is 7, what is the area of the triangle?

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Answer 1 · 2018-04-07T09:33:42

$color(blue)("Area of Triangle " A_t = color(indigo)(33.46 " sq units"$

$hat A = pi/6, hat C = (3pi)/4, b = 7, " To find area of " Delta$

$hat B = pi - pi/6 - (3pi)/ 4 = pi/12$

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

$a / sin (pi/6) = 7 / sin (pi/12) = c / sin ((3pi) / 4)$

$a = (7 * sin (pi/6) ) / sin (pi/12) = 13.52$

Now we know two sides and the included angle.

$:. "Area of " Delta = A_t = (1/2) a b sin C$

$A_t = (1/2) * 13.52 * 7 * sin ((3pi)/4) = color(indigo)(33.46 " sq units"$

A triangle has sides A,B, and C. If the angle between sides A and B is (3pi)/4(3pi)/4, the angle between sides B and C is pi/6pi/6, and the length of B is 7, what is the area of the triangle?