518. - To Find The Versed Sine Of An Arc Of A Circle When The Radius And Chord Are Given
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This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.
518. - To Find The Versed Sine Of An Arc Of A Circle When The Radius And Chord Are Given
The versed sine is equal to the radius, less the square root of the difference of the squares of the radius and half chord; expressed algebraically thus: 
where r is the radius, v the versed sine, and c the chord. (Equation (161.) reduced.)
Example. - In an arc of a circle whose radius is 75 feet, what is the versed sine to a chord of 120 feet? By the table in the Appendix it will be seen that -
The square of the radius, 75, equals ........ | 5625 |
The square of half the chord, 60, equals.... | 5600 |
The difference is ............................................ | 2025 |
The square root of this is ............................ | 45 |
This deducted from the radius ..................... | 75 |
The remainder is the versed sine, = | 30 |
This is expressed bythe formula, thus -
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