A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/3$ . If side C has a length of $6$ and the angle between sides B and C is $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2018-02-25T05:16:36

Length of side $color(green)(a = (c * sin A) / sin C ~~ 6.4$

Length of side $color(blue)(b = (c * sin B) / sin C ~~ 6.869$

$hat C = pi/3, hat A = (3pi)/8, c = 6$

Third $hat B = pi - ((3pi)/8) - pi / 6 = (11pi)/24$

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Applying law of sine,

$color(green)(a = (c * sin A) / sin C = (6 * sin ((3pi)/8)) / sin ((pi)/3) ~~ 6.4$

$color(blue)(b = (c * sin B) / sin C = (6 * sin ((11pi)/24)) / sin (pi/3) ~~ 6.869$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/3(pi)/3. If side C has a length of 6 6 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?