A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/6$ . If side C has a length of $2$ and the angle between sides B and C is $( 5 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2018-02-18T16:19:28

Length of side $color(blue)(a = 3.6955, b = 2.435)$

$hatC = pi/6, hatA = (5pi)/8, c = 2$

To find sides a, b

$hatB = pi - (5pi)/8 - pi/6 = (5pi)/24$

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

$a = (c sin A) / sin C = (2 sin ((5pi)/8)) / sin (pi/6) = 3.6955$

$b = (c sin B) / sin C= (2 * sin ((5pi)/24) ) / sin (pi/6) = 2.435$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6(pi)/6. If side C has a length of 2 2 and the angle between sides B and C is ( 5 pi)/8( 5 pi)/8, what are the lengths of sides A and B?