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,

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

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4(pi)/4. If side C has a length of 15 15 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?