This may be embarrasingly simple, but I haven't been finding what I need out there:
I would like a formula I can use with simple tools (pocket calculator)
to calculate the length of an Arc knowing the length of the Chord and
the Central Angle.
(I'm using these terms as defined on the page http://www.1728.com/circsect.htm)
For example, if I know my Chord is 50 units and that my Central Angle
is 90 degrees (25% of a circle), with this information I would like to
be able to directly calculate the Arc of ~55.54 units. If I could
also find the Radius of ~35.36 units this would be helpful as well to
me, but not necessary to answering the question.
Information/tools I have found useful so far in my search:
"Circle Calculator", http://www.1728.com/circsect.htm
"Chord (geometry) - Wikipedia", http://en.wikipedia.org/wiki/Chord_%28geometry%29
I want to be able to do this calculation in the field, the less
advanced the tools necessary, the better. Acceptable answers, in
order of best to worst:
-Can be solved with pen and paper
-Can be solved with scientific calculator (TI-36x manual;
http://www.radioshack.com/sm-ti-36x-solar-scientific-calculator--pi-2104642_tb-support.html)
-CThis may be embarrassingly simple, but I haven't been finding what I
need out there:
I would like a formula I can use with simple tools (pocket calculator)
to calculate the length of an Arc knowing the length of the Chord and
the Central Angle.
(I'm using these terms as defined on the page http://www.1728.com/circsect.htm)
For example, if I know my Chord is 50 units and that my Central Angle
is 90 degrees (25% of a circle), with this information I would like to
be able to directly calculate the Arc of ~55.54 units. If I could
also find the Radius of ~35.36 units this would be helpful as well to
me, but not necessary to answering the question.
Information/tools I have found useful so far in my search:
"Circle Calculator", http://www.1728.com/circsect.htm
"Chord (geometry) - Wikipedia", http://en.wikipedia.org/wiki/Chord_%28geometry%29
I want to be able to do this calculation in the field, the simpler the
tools needed the better. Acceptable answers, in order of best to
worst:
-Can be solved with pen and paper using simple math
-Can be solved with scientific calculator (TI-36x manual;
http://www.radioshack.com/sm-ti-36x-solar-scientific-calculator--pi-2104642_tb-support.html)
-Can be solved using a Spreadsheet (MS Excel, OpenOffice.org Calc)
Sorry my question is so wordy, I'm trying to define something I don't
understand as well as I want to. If I left anything out you need to
know please ask.an be solved using a Spreadsheet (MS Excel,
OpenOffice.org Calc) |