A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ . If side C has a length of $16$ $16$ 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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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ . If side C has a length of $16$ $16$ 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 · 2018-02-25T05:33:33

$a = \frac{c sin A}{sin C} = \frac{16 \cdot sin (\frac{π}{12})}{sin (\frac{2 π}{3})} \approx 4.78$ $color(green)(a = ( c sin A ) / sin C = (16 * sin (pi/12)) / sin ((2pi)/3) ~~ 4.78$

Explanation:

Law of sines

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Given : c = 16, hat C = (2pi)/3, hat A = pi/12#

To find length of side $a$ $color(green)(a$

Applying Law of Sines,

$a = \frac{c sin A}{sin C} = \frac{16 \cdot sin (\frac{π}{12})}{sin (\frac{2 π}{3})} \approx 4.78$ $color(green)(a = ( c sin A ) / sin C = (16 * sin (pi/12)) / sin ((2pi)/3) ~~ 4.78$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ . If side C has a length of $16$ $16$ 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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A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/32π3(2pi)/3. If side C has a length of 16 1616 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?