Re: How to measure an angle?


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.

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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