A triangle has sides A, B, and C. Sides A and B are of lengths $9$ $9$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{7 π}{8}$ $(7pi)/8$ . What is the length of side C?

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Answer 1 · 2016-11-06T15:48:53

$C = 15.7$ $"C"=15.7$

To answer this question, we have to use the law of cosines.

$C^{2} = A^{2} + B^{2} - 2 AB cos (c) = 81 + 49 - 126 cos (\frac{7}{8} π) = 246.4$ $"C"^2="A"^2+"B"^2-2"AB"cos("c")=81+49-126cos(7/8pi) =246.4$

$C = \sqrt{264.4} = 15.7$ $"C"=sqrt264.4=15.7$

Answer 2 · 2016-11-06T15:54:13

2.0359.....

Cosine rule (rearranged for c) = $c^{2} = a^{2} + b^{2} - 2 a b \cdot cos C$ $c^2 = a^2+b^2-2ab*cosC$

$= c = \sqrt{9^{2} + 7^{2} - 2 \cdot 9 \cdot 7 \cdot cos (\frac{7 π}{8})}$ $=c= sqrt(9^2+7^2-2*9*7*cos( (7pi)/8))$

=2.035924013

A triangle has sides A, B, and C. Sides A and B are of lengths 99 and 77, respectively, and the angle between A and B is 7π8(7pi)/8 . What is the length of side C?