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

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Answer 1 · 2018-02-17T02:52:59

Area of triangle #Delta ABC = (1/2) a c sin B = color(blue)(0.134#

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Given #hatC = pi/12, hatA = pi/12, b = 1#

It’s an isosceles triangle with sides a & c equal, as their angles are equal.

#hatB = pi - pi / 12 - pi / 12 = (5pi)/6#

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

#a / sin ((pi)/12) = c / sin ((pi)/12) = 1/ sin ((5pi)/6)#

#a = c = (1 * sin (pi/12)) / sin ((5pi)/6) = 0.5176#

Area of triangle #Delta ABC = (1/2) a c sin B #

#=> (1/2) * 0.5176 * 0.5176 * sin ((5pi)/6) = color(blue)(0.134#