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 $16$ 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 · 2018-03-26T02:43:16

$color(green)("length of side " a) = (c * sin A) / sin C = color(green)(17.07)$

$color(green)("Length of side " b) = (c * sin B) / sin C = color(green)(2.41)$

$"Given : " hat C = pi/3, c = 16, hat A = (3pi) / 8$

$"To find lengths of sides a & b"$

http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/

$hat B = pi - pi/3 - (5pi)/8 = pi/24$

Applying Law of sines,

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

$color(green)(a) = (c * sin A) / sin C = (16 * sin ((3pi)/8)) / sin(pi/3) = color(green)(17.07)$

$color(green)(b) = (c * sin B) / sin C = (16 * sin (pi/24)) / sin(pi/3) = color(green)(2.41)$

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 16 16 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?