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?
>
> Thanks.

Use a protractor?

But seriously though, in general you will need to use an inverse trig
function. E.g. you know the cosine of the angle (say from the cosine
rule or similar), and you need to find the angle. (In certain special
cases the angle is obvious by inspection. For example, if ABC is an
equilateral triangle.)

But the actual values of inverse trig functions ARE calculated using
"numeric methods", whether you use tables or a calculator. How else
could they be found? For a flavour of this, see for example formula 19
at http://mathworld.wolfram.com/InverseCosine.html.

When you use a calculator, the calculator has some numerical recipe
built in to it (not necessarily exactly that formula... one that is
especially efficient - i.e. converges especially rapidly for the given
value - will have been chosen).

Prior to calculators, some poor soul when through the slog of
hand-calculating the answers using some numerical method or other. If
you really wanted to you could do the same hand calculations yourself.

.

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