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 $2$ 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 · 2018-03-16T09:43:04

Lengths of sides $color(brown)(a ~~ 2.13, b = 1.83$

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

Given : $hat A = (3pi) / 8, hat C = pi / 3, c = 2$

$hat B = pi - (3pi)/8 - pi/3 = (7pi)/24$

$a / sin ((3pi)/8) = b / sin ((7pi)/24) = 2 / sin pi/3$

$a = (2 * sin ((3pi)/8) ) / sin (pi/3) ~~ 2.13$

$b = (2 * sin ((7pi)/24) ) / sin (pi/3) ~~ 1.83$

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 2 2 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?