Re: How to measure an angle?


Randy Poe wrote:
> Albert wrote:
> > Hello,
> >
> > sorry for dubious question, but could someone advise how to measure in
> > degrees an angle ABC with numeric methods (i.e. without trigonometric
> > tables) when one knows the coordinates of points A, B and C? I know
> > that one can measure any trigonometric function of the angle and after
> > that to look up the corresponding value in degrees in the trigonometric
> > table. But is there a way to measure an angle without trigonometric
> > tables?
>
> By dot product.
>
> Let u_BA = unit vector from B to A = (A-B)/|A-B|
>
> (vector difference A-B, divided by magnitude of the
> vector B-A)
>
> Let u_BC = unit vector from B to C = (B-C)/|B-C|
>
> Then cos(ABC) = u_BA (dot) u_BC
>
> ABC is the arccossine of the dot product, which you can find
> with a computer or calculator.

Or trig tables perhaps?

>
> To take the dot product of two vectors, multiply corresponding
> components and add:
>
> (x1,y1) dot (x2,y2) = (x1*x2 + y1*y2)
>
> - Randy

.

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