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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 15, what is the area of the triangle?

1 Answer

Aug 10, 2018

#color(maroon)(A_t = 1/2 a b sin C ~~ 35.66# sq. units

Explanation:

#hat A = pi/4, hat C = pi/12, hat B = pi - pi/4 - pi/12 = (2pi)/3, b = 15#

Law of sines : #a / sin A = b / sin B = c / sin C#

#a = (b sin A) / sin B = (15 * sin (pi/12)) / sin (pi/4) ~~ 5.49#

Area of #Delta = A_t = 1/2 a b sin C #

#color(maroon)(A_t = 1/2 * 5.49 * 15 sin ((2pi)/3) ~~ 35.66# sq. units

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