A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/12#, the angle between sides B and C is #(5pi)/6#, and the length of side B is 9, what is the area of the triangle?

Question

1463 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-15T15:14:39

#81 /4#

We use ABC for points; and a,b,c for opposite sides.

angle between a and b = #hat C = 1/12 pi#

angle between b and c = #hat A = 5/6 pi#

#hat B = pi - hat C - hat A = pi (1 - 1/12 - 5/6) = 1/12 pi = hat C#

Therefore, #c = b = 9#.

Let #H = (B + C)/2.#

enter image source here

We want #S_Delta = 1/2 * a * h#

#sin hat C = h/9# AND #cos hat C = a/18#

#S_Delta = 1/2 * 18 cos hat C * 9 sin hat C = 81/2 sin frac{pi}{6} = 81/2 * 1/2#