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A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/6#, the angle between sides B and C is #(2pi)/3#, and the length of side B is 25, what is the area of the triangle?

1 Answer

sankarankalyanam

Apr 10, 2018

#:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"#

Explanation:

#hat A = (2pi)/3, hat C = pi/6, hat B = pi - pi/6 - (2pi)/3 = pi/3, b = 25#

It's an isosceles triangle with sides b & c equal.

#:. c = b = 25#

#color(blue)("Area of " Delta " " A_t = (1/2) * b * c * sin A#

#:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"#

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