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 $26$ $26$ 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 $26$ $26$ 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 · 2018-05-06T04:34:20

$Length of side a = 7.77 units$ $color(indigo)("Length of side a " = 7.77 " units"$

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{2 π}{3}, ˆ B = π - \frac{π}{12} - \frac{2 π}{3} = \frac{π}{4}, c = 26$ $hat A = pi/12, hat C = (2pi)/3, color(red)(hat B = pi - pi/12 - (2pi)/3 = pi/4, c = 26$

$According to Lw of sines, \frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $color(maroon)("According to Lw of Sines, " a / sin A = b / sin B = c / sin C$

$a = \frac{c \cdot sin A}{sin C} = \frac{26 \cdot sin (\frac{π}{12})}{sin (\frac{2 π}{3})} \approx 7.77$ $a = (c * sin A) / sin C = (26 * sin (pi/12)) / sin ((2pi)/3) ~~ 7.77$

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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 $26$ $26$ 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 2π3(2pi)/3. If side C has a length of 2626 and the angle between sides B and C is π12pi/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 $26$ $26$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?