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A triangle has sides A, B, and C. The angle between sides A and B is #pi/4# and the angle between sides B and C is #pi/12#. If side B has a length of 35, what is the area of the triangle?

1 Answer

sankarankalyanam

Apr 7, 2018

#color(blue)("Area of " Delta " " A_t = 129.44#

Explanation:

#hat B = pi - hat A - hat C = pi - pi/12 - pi/4 = (2pi)/3#

As per the Law of Sines,

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

#a = (35 * sin (pi/12)) / sin ((2pi)/3) = 10.46#

#color(green)("Area of Triangle " A_t = (1/2) a b sin C#

#A_t = (1/2) * 10.46 * 35 * sin(pi/4) = 129.44#

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