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?

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Answer 1 · 2018-08-10T13:21:57

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

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

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

A triangle has sides A, B, and C. The angle between sides A and B is pi/4pi/4 and the angle between sides B and C is pi/12pi/12. If side B has a length of 15, what is the area of the triangle?