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Sub-Page for Programming Challenge (Drawing Angles, Maps) Page

Gives the answer to a question posed there

If you haven't come here from my page with a programming challenge, it would be best to go there NOW. You will get a chance to return here, when the appropriate time comes.

The "trick to seeing the answer to "how do we get "the number" comes in two parts.

Start with "What would the number be if AB were 1cm?"

Remember that we know, from sine tables, that in the following, if AC is 1cm, then BC is 0.38cm


But! When we wanted to draw a 40 degree angle, we didn't even have a triangle, let alone a right angle! To do sines (directly) we need a right angle.

Look at...


I hope you said "Ah!"? (If not, study the diagram again.)

We aren't going to try to draw CAB and BAD, but do you see how each of them is a right angle triangle, with a 30 degree angle? As such, if AC and AD are each 1cm long, then CB and BD are each 0.38cm long, and thus we know that the chord (CD) of a 60 degree angle, at a radius of 1cm, is 0.68cm.

That's the hard part done. Go back and re-read it until you really understand it. Properly!

That's all well and good, if AC is 1cm. What if it isn't? Easy! The number we want (the length of AD) is directly proportional to the length of AC. (If AC is 5.28 cm, then AD is 5.28 times what it was when AC was 1cm.)

Here's a link to the main page of this discussion... but if you came here from there, just close this page... the page you came from should be "underneath" this page.

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I have other sites. My Google custom search button will include things from them....
   One of my SheepdogGuides pages.
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