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 $19$ 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 · 2018-02-18T13:06:34

Length of side $color(blue)(a = 35.1074)$

Length of side $color(blue)(b = 23.1329)$

$hatA = (5pi)/8, hatC = pi/6, c = 19$

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

$a / sin A = b / sin B = c / sin C$ . Law of sines

$a = ((c * sin A) / sin C )= (19 * sin ((5pi)/8) ) / sin (pi/6) = color(green)(35.1074)$

$b = ((c * sin B) / sin C )= (19 * sin( (5pi)/24) ) / sin (pi/6) = color(green)(23.1329)$

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 19 19 and the angle between sides B and C is ( 5 pi)/8( 5 pi)/8, what are the lengths of sides A and B?