Plane trigonometry, by S.L. Loney.

MEASUREMENT OF ANGLES.

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In practice it is generally found more convenient to
reduce any angle to a fraction of a right angle. The
method will be seen in the following examples;
Ex. 1. Reduce 63~14' 51" to Centesimal MJeasure.
We have 51" = 85',
14.850
and 14 51" 14'85'=485 = 2475~,
60
63-2475. 63~ 14'51" = 63-24750 = 7rt. angle
90
= 70275 rt. angle
= 70'275= 70 275' = 70 27' 50.
Ex. 2. Reduce 94 23' 87" to Sexagesimal Mleasure.
94g 23' 87"= 942387 right angle
90
84-81483 degrees
60
48-8898 minutes
60
53-3880 seconds. 94s 23' 87" = 84~ 48' 53-388".
6. Angles of any size.
Suppose AOA' and BOB' to be two fixed lines meeting
at right angles in 0, and suppose
a revolving line OP (turning about p pl
a fixed point at 0) to start from
OA and revolve in a direction / P
opposite to that of the hands of a A^ A
watch.
For any position of the re- P\ P4
volving line between OA and OB,
such as OP1, it will have turned
through an angle AOP1, which is less than a right angle.
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