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 9, what is the area of the triangle?

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Answer 1 · 2018-04-08T01:59:18

$color(green)("Area of Triangle " color(maroon)(A_t = 8.56 color(green)(" sq units")$

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$hat A = pi/12, hat C = pi/4, b = 9$

$hat B = pi - pi/12 - pi/4 = (2pi)/3$

a = (b * sin A) / sin B = (9 * sin (pi/12)) / sin ((2pi)/3) = 2.69#

Area of triangle, known two sides and the included angle is

$A_t = (1/2) a b sin C = (1/2) * 2.69 * 9 * sin (pi/4) = 8.56$

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 9, what is the area of the triangle?