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 8, what is the area of the triangle?

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Answer 1 · 2018-05-26T01:35:42

Area of triangle $color(maroon)(A_t = 16$ sq units

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

$b = 8, hat A = pi/12, hat C = (5pi)/6$

$hat B = pi - pi/12 - (5pi)/6 = pi/12$

It’s an isosceles triangle with sides a and b equal.

$:. a = b = 8$ units

Area of triangle $A_t = (1/2) * 8 * 8 * sin ((5pi)/6)$

$A_t = 16$

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 8, what is the area of the triangle?