A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4#. If side C has a length of #15 # 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 · 2018-03-26T03:25:07

#color(blue)(a = b = (c * sin A) / sin C) = color(blue)(19.6 " units"#

To find sides a, b.

#Given : hat A = (3pi)/8, hat C = pi/4, c = 15#

#hat B = pi - (3pi)/8 - pi/4 = (3pi)/8#

It's an isosceles triangle with sides angles #hatA & hatB = (3pi)/8#

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

Applying Law of Sines,

#color(blue)(a = b = (c * sin A) / sin C) = (15 * ((3pi)/8)) / sin (pi/4) = color(blue)(19.6 " units"#