A triangle has sides A,B, and C. If the angle between sides A and B is #(2pi)/3#, the angle between sides B and C is #pi/6#, and the length of B is 2, what is the area of the triangle?

Question

1431 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-17T02:00:50

#A_b = color(blue)(1.732#

Sum of the three angles of a triangle #= pi^c#

Hence the third angle #hatB = pi - (2pi)/3 - pi/6 = pi/6#

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

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

When length 2 corresponds to #/_B = /_(pi/6)#

#a/ sin (pi/6) = 2 / sin (pi/6) = c / sin ((2pi)/3)#

#:. a = 2, c = (2 sin ((2pi)/3)) / sin (pi/6) = 3.4641#

Area of triangle #A-b = (1/2) * ac sin B = (1/2) * 2 * 3.4641 * sin (pi/6) = 1.732#