A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $9$ $9$ and the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $9$ $9$ and the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , what are the lengths of sides A and B?

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Answer 1 · 2018-02-26T14:24:19

Length of sides $a = 17.3867, b = 12.7279$ $color(brown)(a = 17.3867, b = 12.7279)$

Explanation:

Given : $ˆ C = \frac{π}{6}, ˆ A = \frac{7 π}{12}, c = 9$ $hat C = pi/6, hat A = (7pi)/12, c = 9$

$ˆ B = π - \frac{7 π}{12} - \frac{π}{6} = \frac{π}{4}$ $hat B = pi - (7pi)/12 - pi / 6 = pi / 4$

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Applying law of sines,

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

$b = \frac{c sin B}{sin C} = \frac{9 \cdot sin (\frac{π}{4})}{sin (\frac{π}{6})} = 12.7279$ $b = (c sin B) / sin C = (9 * sin (pi/4)) / sin (pi/6) = 12.7279$

$a = \frac{b sin A}{sin B} = \frac{12.7279 \cdot sin (\frac{7 π}{12})}{sin (\frac{π}{4})} = 17.3867$ $a = (b sin A) / sin B = (12.7279 * sin ((7pi)/12)) / sin (pi/4) = 17.3867$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $9$ $9$ and the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is π6(pi)/6. If side C has a length of 99 and the angle between sides B and C is 7π12(7pi)/12, what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $9$ $9$ and the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , what are the lengths of sides A and B?