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is it possible to find the third side of a triangle if you know the lengths of the other two and the angle between the known sides? the triangle is not equilateral.

we're using the kinect camera and we can find the distance from the camera to the start of a line and the distance to the end of a line, we could calculate the angle between the two lines knowing the maximum vertical and horizontal angle but would it be possible to calculate the length of the line on the ground? the problem is that the camera won't be exactly above the line so the triangle we get wouldn't be equilateral.

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Yes, you can use the law of cosines... –  J. M. Apr 19 '12 at 17:22

4 Answers 4

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How about the law of cosines?

Consider the following triangle $\triangle ABC$, the $ \color{maroon} {\text{poly 1}}$ below, with sides $\color{maroon}{\overline{AB}=c}$ and $\color{maroon}{\overline{AC}=b}$ known. Further the angle between them, $\color{green}\alpha$ is known.

$\hskip{2 in}$Triangle

Then, the law of cosines tell you that $$\color{maroon}{a^2=b^2+c^2-2bc\;\cos }\color{green}{\alpha}$$

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This is precisely what the cosine theorem allows you to compute: $$c^2 = a^2 + b^2 - 2ab\cos(\gamma)$$ where $\gamma$ is the angle opposite to $c$

(uhm, yes, is probably be called 'law of cosine' rather than 'cosine theorem').

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Use the law of cosines...

$c^2 = a^2 + b^2 - 2ab \cdot \cos{\theta}$

... where $a$ and $b$ are the sides you know, $\theta$ the angle between them, and $c$ the side you seek, opposite $\theta$.

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If you are interested in doing calculations with specific angles and sides when there is information which forces a specific triangle, as is true in Euclidean geometry with angle-side-angle, rather than "theory" you can do this at this on-line site: http://www.calculatorsoup.com/calculators/geometry-plane/triangle-theorems.php

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