A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ . If side C has a length of $24$ $24$ 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 $\frac{3 π}{4}$ $(3pi)/4$ . If side C has a length of $24$ $24$ 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 · 2018-02-18T12:35:34

Lengths of sides $a = 8.7846, b = 16.9706$ $color(red)(a = 8.7846, b = 16.9706$

Explanation:

Given : $ˆ A = \frac{π}{12}, ˆ C = \frac{3 π}{4}, c = 24$ $hatA = pi/12, hat C = (3pi)/4, c = 24$

To find $a, b$ $a, b$

Third angle $ˆ B = π - \frac{3 π}{4} - \frac{π}{12} = \frac{π}{6}$ $hat B = pi - (3pi)/4 - pi/12 = pi/6$

By the law of sines,

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

$a = \frac{c \cdot sin A}{sin C} = \frac{24 \cdot sin (\frac{π}{12})}{sin (\frac{3 π}{4})} = 8.7846$ $a = (c * sin A) / sin C = (24 * sin (pi/12)) / sin ((3pi)/4) = color(purple)(8.7846)$

$b = \frac{c \cdot sin B}{sin C} = \frac{24 \cdot sin (\frac{π}{6})}{sin (\frac{3 π}{4})} = 16.9706$ $b = (c * sin B) / sin C = (24 * sin (pi/6)) / sin ((3pi)/4) = color (purple)(16.9706$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ . If side C has a length of $24$ $24$ 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 3π4(3pi)/4. If side C has a length of 2424 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 $\frac{3 π}{4}$ $(3pi)/4$ . If side C has a length of $24$ $24$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?