A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{8}$ $pi/8$ . If side C has a length of $21$ $21$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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Answer 1 · 2018-03-23T11:37:56

$Side a \approx 14.2$ $color(brown)(" Side " a ~~ 14.2$

![http://olympics321.weebly.com/http://law-of-cosines-and-sines.html](https://useruploads.socratic.org/8GEr7ZWeTO200Akp51fD_law%20of%20sine.jpg)

Applying Law of Sine :

$\frac{a}{sin A} = \frac{c}{sin C}$ $a / sin A = c / sin C$

$a = \frac{c \cdot sin A}{sin C} = \frac{21 \cdot sin (\frac{π}{12})}{sin (\frac{π}{8})}$ $a = (c * sin A) / sin C = (21 * sin (pi/12) )/ sin (pi/8)$

$a = \frac{21 \cdot 0.2588}{0.3827} = 14.2029$ $a = (21 * 0.2588) / 0.3827 = color(green)(14.2029)$

A triangle has sides A, B, and C. The angle between sides A and B is π8pi/8. If side C has a length of 2121 and the angle between sides B and C is π12pi/12, what is the length of side A?