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?

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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 $H = (B + C)/2.$

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

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

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

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