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

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Answer 1 · 2018-02-17T09:14:37

Area of right triangle #A_t = color (red)(4.5#

#hatA = pi/12, hatC = (5pi)/12, b = 6#

#hat B = pi - pi/12 - (5pi)/12 = pi/2#

It’s a right triangle.

#a/ sin A = b / sin B = c / sin C#

#a = (6 * sin (pi/12)) / sin (pi/2) = 1.5529#

#c = 6 * sin ((5pi)/12) = 5.7956#

Area of right triangle A_t = (1/2) a c = (1/2) * 1.5529 * 5.7956 = 4.5#