Looking for Central Angle

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Billvt

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Jan 11, 2011
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need help figuring out the central angle of an isoseles triangle formed by two radius arms and a chord when the radius and the chord lengths are known. I split the triangle to get a right triangle and then tried the formula: Angle = arccos ((a^2 + b^2 - c^2)/2ab) and cannot seem to get a good answer. Tried a 3,4,5 right triangle and cannot seem to get 30 degrees. Any one know what I am doing wrong?
 
Hello, Billvt!

Need help figuring out the central angle of an isoseles triangle formed by two radius arms and a chord
when the radius and the chord lengths are known.

\(\displaystyle \text{I split the triangle to get a right triangle and then tried the formula: }\:\angle C \:=\:\arccos\left(\frac{a^2 + b^2 - c^2}{2ab}\right)\:\text{ and cannot seem to get a good answer.}\)

Tried a 3,4,5 right triangle and cannot seem to get 30 degrees. . Of course not!

Any one know what I am doing wrong?
Click to expand...

A 3-4-5 right triangle does not have a 30-degree angle.

\(\displaystyle \text{If the radius is }r\text{ and the length of the chord is }c\text{, then we can use: }\:\theta \:=\:\arccos\left(\frac{2r^2-c^2}{2r^2}\right)\)

 
pka - thank you for post of the wiki re circular segment, it seems the additional height of the segment beyond the chord would have to be known to get enough information to obtain the central angle from these formulas.
 
soroban - thank you for your post as well - are you saying that the isoslese triangle does NOT have to be split in order to use the formula? And thank you for clarifying that a 3,4,5 triangle is not 30,60,90, a mis-conception of mine. Can you give me a known scenario so I can check the math on Microsoft Excel?
 
soroban - can I also assume that the result to the equation you gave me is in radians that needs to be converted?
 
for all - I am building a geodesic dome and trying to determine the angles between the struts from the point where the struts come together - the points where they meet are all a radius away from the center, so the angle is dependent upon the chord length and thus my question.
 
A dome will be 3-D structure. The equation provided by Soroban is valid for a planar structure. Angles and lengths will change in the projected 2-D view.
 
Thank you Subhotosh - please correct me if I am wrong - for each strut a 2-D calculation should be sufficient, should it not?
 
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