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 $18$ $18$ 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 $18$ $18$ 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 · 2016-03-08T17:02:15

$a \approx 6.59, b \approx 12.73$ $a~~6.59, b~~12.73$

Explanation:

$\frac{a}{sin (\frac{π}{12})} = \frac{18}{sin (\frac{3 π}{4})}$ $a/sin(pi/12) =18/sin ((3pi)/4)$
$a = \frac{18}{sin (\frac{3 π}{4})} \cdot sin (\frac{π}{12}) \approx 6.59$ $a=18/sin ((3pi)/4)*sin(pi/12)~~6.59$
$∠ B = π - [(\frac{3 π}{4}) + \frac{π}{12}] = \frac{π}{6}$ $angleB = pi-[((3pi)/4)+pi/12]=pi/6$
$\frac{b}{sin (\frac{π}{6})} = \frac{18}{sin (\frac{3 π}{4})} \to b = \frac{18}{sin (\frac{3 π}{4})} sin (\frac{π}{6}) \approx 12.73$ $b/sin(pi/6) =18/sin ((3pi)/4) ->b=18/sin ((3pi)/4) sin(pi/6) ~~12.73$

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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 $18$ $18$ 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 $18$ $18$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?