A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{7 π}{8}$ $(7pi)/8$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 12, what is the area of the triangle?

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Answer 1 · 2018-04-07T04:22:49

$color(green)("Area of " Delta " " A_t = 54.62 " sq units"$

$hat A = pi/12, hat C = (7pi)/8, b = 12, " To find the area of " Delta$

$hat B = pi - hat A - hat C = pi - pi/12 - (7pi)/8 = pi/24$

![https://www.teacherspayteachers.com/Product/Law-of-Sine-and-Law-of-Cosine-Foldable-For-Oblique-Triangles-716112]( useruploads.socratic.org )

$a / sin (pi/12) = 12 / sin(pi/24) = c / sin ((7pi)/8)$

$a = (12 * sin (pi/12)) / sin (pi/24) = 23.79$

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/rQbBkYmuS2aENL6Uef1c_area%20of%20triangle.png)

Knowing two sides a,b and the included angle C, to find the area we can use the formula $color(crimson)(A_t = (1/2) a b sin C$

$A_t = (1/2) * 23.79 * 12 * sin((7pi)/8) = color(purple)(54.62 " sq units"$

A triangle has sides A,B, and C. If the angle between sides A and B is (7pi)/87π8(7pi)/8, the angle between sides B and C is pi/12π12pi/12, and the length of B is 12, what is the area of the triangle?