A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/6# and the angle between sides B and C is #pi/6#. If side B has a length of 2, what is the area of the triangle?

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Answer 1 · 2018-03-27T03:53:38

#color(indigo)(Delta " " A_t = (1/2) ab sin C = 0.575 " sq units"#

#hat A = pi/6, hat C = pi/6, b = 2#

To find the area of the isosceles triangle.

#hat B = pi - pi/6 - pi/6 = (2pi)/3#

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

#a = (b * sin A) / sin B = (2 * sin (pi/6)) / sin ((2pi)/3) = 1.15 " units"#

#Delta " " A_t = (1/2) ab sin C = (1/2) * 1.15 * 2 * sin (pi/6) = 0.575#