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: 518 To Find The Versed Sine Of An Arc Of A Circle  535 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 -

518 To Find The Versed Sine Of An Arc Of A Circle  536