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 $24$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2018-03-26T02:28:37

$color(blue)("Length of side " a = 4.39 " units$

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

$hat C = pi/4, hat A = pi/12, c = 24, " To find a"$

Applying Lwa of Sines,

$a / sin A = c / sin C$

$a = (c * sin A) / sin C = (24 * sin (pi/12)) / sin (pi/4)$

$a = (24 * 0.2588) / (1/sqrt2) = 24 * 0.2588 * 0.707 = 4.39$

A triangle has sides A, B, and C. The angle between sides A and B is pi/4pi/4. If side C has a length of 24 24 and the angle between sides B and C is pi/12pi/12, what is the length of side A?