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/12#. If side B has a length of 25, what is the area of the triangle?

1 Answer
sankarankalyanam
May 3, 2018

#color(maroon)("Area of Triangle " A_t = 57.2 " sq units"#

Explanation:

#color(blue)("Given " hat A = pi/12, hat C = pi/6, hat B = pi - pi/12 - pi/6 = (3pi)/4, b = 25#

#"As per " color(red)("Law of Sines", color(green)(a / sin A = b / sin B = c / sin C#

#a / sin (pi/12) = 25 / sin ((3pi)/4) = c / sin (pi/6)#

#c = (25 * sin (pi/6)) / sin ((3pi)/4) = 17.68#

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

#A_t = (1/2) * 25 * 17.68 * sin (pi/12) = 57.2 " sq units"#

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