A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $14$ $14$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , 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 $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $14$ $14$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?

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Answer 1 · 2018-02-18T12:51:56

Lengths of sides $a = b = 7.2469$ $color(brown)(a = b = 7.2469)$

Explanation:

To find the lengths of sides a, b.

Given $ˆ A = \frac{π}{12}, ˆ C = \frac{5 π}{6}, c = 14$ $hatA = pi/12, hatC = (5pi)/6, c = 14$

Third angle $ˆ B = π - \frac{π}{12} - \frac{5 π}{6} = \frac{π}{12}$ $hat B = pi - pi/12 - (5pi)/6 = pi/12$ by the law of sines.

As $ˆ B = ˆ C$ $hat B = hat C$ , it’s an isosceles triangle, with sides a, b equal.

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

$a = b = \frac{c \cdot sin A}{sin C} = \frac{14 \cdot \frac{sin (π)}{12}}{sin (\frac{5 π}{6})} = 7.2469$ $a = b = (c * sin A) / sin C = (14 * sin (pi)/12) / sin ((5pi)/6) = color(brown)7.2469$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $14$ $14$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , 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 5π6(5pi)/6. If side C has a length of 1414 and the angle between sides B and C is π12pi/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 $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $14$ $14$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?