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"#

#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)#