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 #25 # 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 · 2018-04-11T11:28:02

#color(indigo)("Length of side " = a = b = 6.53 " units"#

#hat A = (3pi)/8, hat C = pi/4, c = 25, " To find a & b"#

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

It's an isosceles triangle with sides a & b equal.

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

#:. a = b = (c * sin B) / sin C = (25 * sin ((3pi)/8)) / sin (pi/4)#

#color(indigo)(a = b = 6.53 " units"#