A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/12# and the angle between sides B and C is #pi/12#. If side B has a length of 36, what is the area of the triangle?

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Answer 1 · 2018-04-10T02:53:10

#:.color(brown)(A_t = (1/2) * a * c = (1/2) * 9.32 * 34.77 = 162.06 " sq units"#

#hat A = pi/12, hat C = (5pi)/12, hat B = pi - pi/12 - (5pi)/12 = pi/2, b = 36#

It's a right triangle with #hat B = 90^@#

#color(purple)(a / sin A = b / sin B = c / sin C)#

#:. a = (b * sin A) / sin B = (36 * sin (pi/12)) / sin (pi/2) = 9.32#

#:. c = (b * sin C) / sin B = (36 * sin ((5pi)/12)) / sin (pi/2) = 34.77#

#:.color(brown)(A_t = (1/2) * a * c = (1/2) * 9.32 * 34.77 = 162.06 " sq units"#