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 8, what is the area of the triangle?

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Answer 1 · 2018-05-26T01:35:42

Area of triangle #color(maroon)(A_t = 16# sq units

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

#b = 8, hat A = pi/12, hat C = (5pi)/6#

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

It’s an isosceles triangle with sides a and b equal.

#:. a = b = 8# units

Area of triangle #A_t = (1/2) * 8 * 8 * sin ((5pi)/6)#

#A_t = 16#