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 $15$ $15$ 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 $15$ $15$ 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 · 2017-04-11T06:06:57

$A = 28.978$ $A = 28.978$
$B = 21.213$ $B = 21.213$

Explanation:

Angle of $A = \frac{7 π}{12}, C = \frac{π}{6}$ $A = (7 pi)/12, C = pi/6$ , therefore angle of $B = π - \frac{7 π}{12} - \frac{π}{6} = \frac{3 π}{12}$ $B = pi - (7 pi)/12 -pi/6 = (3 pi)/12$

we use a formulae, $\frac{A}{sin A} = \frac{B}{sin B} = \frac{C}{sin C}$ $A / sin A = B / sin B = C / sin C$

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

$\frac{A}{sin (\frac{7 π}{12})} = \frac{15}{sin (\frac{π}{6})}$ $A / sin ((7 pi)/12) = 15 / sin (pi/6)$

$A = \frac{15}{sin (\frac{π}{6})} \cdot sin (\frac{7 π}{12}) = \frac{15}{0.5} \cdot 0.966 = 28.978$ $A = 15 / sin (pi/6) * sin ((7 pi)/12) =15 / 0.5 * 0.966 = 28.978$

$\frac{B}{sin B} = \frac{C}{sin C}$ $B / sin B = C / sin C$

$\frac{B}{sin (\frac{3 π}{12})} = \frac{15}{sin (\frac{π}{6})}$ $B / sin ((3 pi)/12) = 15 / sin (pi/6)$

$B = \frac{15}{sin (\frac{π}{6})} \cdot sin (\frac{3 π}{12}) = \frac{15}{0.5} \cdot 0.707 = 21.213$ $B = 15 / sin (pi/6) * sin ((3 pi)/12) = 15/0.5 *0.707= 21.213$

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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 $15$ $15$ 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 1515 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 $15$ $15$ and the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , what are the lengths of sides A and B?