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 $27$ $27$ 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 $27$ $27$ 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 · 2018-05-24T05:27:58

Lengths of sides $a = b = 2.7$ $color(crimson)(a = b = 2.7$ units

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{5 π}{6}, c = 27, a = ?, b = ?$ $hat A = pi/12, hat C = (5pi)/6, c = 27, a = ?, b = ?$

$ˆ B = π - \frac{5 π}{6} - \frac{π}{12} = \frac{π}{12}$ $hat B = pi - (5pi)/6 - pi/12 = pi /12$

It’s an isosceles triangle with sides a & b equal as angles are equal.

According to the law of Sines,

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

$a = b = \frac{c sin A}{sin C} = \frac{27 \cdot sin (\frac{π}{12})}{sin (\frac{5 π}{6})}$ $a = b = (c sin A ) / sin C = (27 * sin (pi/12)) / sin ((5pi)/6)$

$a = b = 2.7$ $color(crimson)(a = b = 2.7$ units

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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 $27$ $27$ 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 (5pi)/65π6(5pi)/6. If side C has a length of 27 2727 and the angle between sides B and C is pi/12π12pi/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 $27$ $27$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?