A triangle has sides A, B, and C. Sides A and B are of lengths $6$ $6$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{7 π}{12}$ $(7pi)/12$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $6$ $6$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{7 π}{12}$ $(7pi)/12$ . What is the length of side C?

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Answer 1 · 2016-03-11T09:27:29

C = $\sqrt{61 + 15 \sqrt{2} (\sqrt{3} - 1)}$ $sqrt( 61 + 15sqrt2(sqrt3-1)$

Explanation:

$C^{2} = A^{2} + B^{2} - 2 A B cos (7 \frac{π}{12}) = 61 - 60 cos (7 \frac{π}{12})$ $C^2 = A^2 + B^2 - 2A B cos (7pi/12) = 61-60 cos(7pi/12)$ $cos (7 \frac{π}{12}) = cos (4 \frac{π}{12} + 3 \frac{π}{12}) = cos (\frac{π}{4} + \frac{π}{3})$ $cos(7pi/12) = cos (4pi/12+3pi/12) = cos (pi/4+pi/3)$

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A triangle has sides A, B, and C. Sides A and B are of lengths $6$ $6$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{7 π}{12}$ $(7pi)/12$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths 66 and 55, respectively, and the angle between A and B is 7π12(7pi)/12 . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $6$ $6$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{7 π}{12}$ $(7pi)/12$ . What is the length of side C?