A triangle has sides A, B, and C. Sides A and B are of lengths $4$ $4$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{2 π}{3}$ $(2pi)/3$ . What is the length of side C?

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Answer 1 · 2017-11-18T20:45:34

$C = \sqrt{93} \approx 9.64$ $C=sqrt(93)~~9.64$

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Using the Cosine Rule:

$C^{2} = B^{2} + A^{2} - 2 B A \cdot cos (c)$ $C^2=B^2+A^2-2BA*cos(c)$

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

$\to C^{2} = 49 + 16 - (56 \cdot - \frac{1}{2}) = 93$ $->C^2=49+16-(56*-1/2)=93$

$C = \sqrt{93} \approx 9.64$ $C=sqrt(93)~~9.64$

A triangle has sides A, B, and C. Sides A and B are of lengths 44 and 77, respectively, and the angle between A and B is 2π3(2pi)/3 . What is the length of side C?