A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/6$ and the angle between sides B and C is $pi/12$ . If side B has a length of 3, what is the area of the triangle?

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Answer 1 · 2018-06-03T01:32:46

Area $color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25$ sq units

Law of Sines $a / sin A = b / sin B = c / sin C$

Area of triangle $A_t =.(1/2) a b sin C$

$b = 3, hat A = pi/12, hat C = (5pi)/6, hat B = pi - pi / 12 - (5pi)/6 = pi/12$

It’s an isosceles triangle with angles #hat A = hat B = pi/12%

$:. b = a = 3$

Area $color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25$ sq units

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6(5pi)/6 and the angle between sides B and C is pi/12pi/12. If side B has a length of 3, what is the area of the triangle?