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

1 Answer
sankarankalyanam
Apr 7, 2018

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

Explanation:

#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

Applying the Law of Sines,

#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/area-triangle.html

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"#

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