A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/6# and the angle between sides B and C is #pi/12#. If side B has a length of 3, what is the area of the triangle?

1 Answer
Kalyanam S.
Jun 3, 2018

Area #color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25# sq units

Explanation:

Law of Sines #a / sin A = b / sin B = c / sin C#

Area of triangle #A_t =.(1/2) a b sin C#

#b = 3, hat A = pi/12, hat C = (5pi)/6, hat B = pi - pi / 12 - (5pi)/6 = pi/12#

It’s an isosceles triangle with angles #hat A = hat B = pi/12%

#:. b = a = 3#

Area #color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25# sq units

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