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 1, what is the area of the triangle?

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Answer 1 · 2018-02-15T15:41:56

Area of right $Delta ABC = color(green)(0.125$

Given $hatA = pi/12, b = 1, hat C = (5pi)/13$

Third angle $hat B = pi - (5pu)/12 - pi / 12 = pi/2$

Hence it’s a right triangle.

$a / sin A = b / sin B = c / sin C$

$a / sin (pi/12) = 1 / sin (pi/2) = c / sin ((5pi)/12) = 1$ , since $sin (pi/2) = 1$

$a = sin (pi/12) = 0.2588$

$c = sin ((5pi)/12) = 0.9659$

Area of right $Delta ABC = (1/2) a c = (1/2) * 0.2588 * 0.9659 = color(green)(0.125$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12(5pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 1, what is the area of the triangle?