A triangle has sides A,B, and C. If the angle between sides A and B is $pi/3$ , the angle between sides B and C is $pi/12$ , and the length of B is 1, what is the area of the triangle?

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Answer 1 · 2018-05-19T16:38:44

$color(blue)(A_t = 0.4019$ sq units

$hat A = (pi)/12, hat C = pi/3, hat B = pi - pi/12 - pi/3 = (7pi)/12, b = 1$

Applying Law of Sines,

$a / sin A = b / sin B$

$a = (1 * sin (pi/12))/sin ((7pi)/12)$

$a = 0.2679$

Area of Triangle $A_t = (1/2) a b sin C$

$A_t = (1/2) * 0.2679 * 1 * sin (pi/3)$

$color(blue)(A_t = 0.4019$ sq units

A triangle has sides A,B, and C. If the angle between sides A and B is pi/3pi/3, the angle between sides B and C is pi/12pi/12, and the length of B is 1, what is the area of the triangle?