Math CentralQuandaries & Queries


Question from Robert:

Can you please tell me if there is a formula to figure out the Sagitta of an
arc when you know the radius, chord length, and arc length?


I'm curious: Did this question arise from a history course? I had to look up the word in the Oxford English Dictionary. It turns out that sagitta is an obsolete term for the versed sine (or versine), which is itself nearly an obsolete concept. By definition,

versin (x) = 1 - cos(x).

Use the radius and half the chord length to find the sine, and from that the cosine; then subtract the cosine from 1. The arc length information is redundant.




Another approach uses the Pythagoran theorem.


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