Plane trigonometry, by S.L. Loney.

THE RADIAN. 13
10 r7
Hence 1(0 (60y): (60+y):: 40: r,
9 1-80
20060-y _40
r 60+y 7r'
i.e. 5 (60-y) =60+ty,
i.e. y=40.
The angles are therefore 20~, 60~, and 100~.
Ex. 2. Exprless in the 3 systems of angular measurement the magnlitude of the angle of a regular decagon.
The corollary to Euc. I. 32 states that all the interior angles of any
rectilinear figure together with four right angles are equal to twice as
many right angles as the figure has sides.
Let the angle of a decagon contain x right angles, so that all the
angles are together equal to 10x right angles.
The corollary therefore states that
10x+4 = 20,
8
so that x= right angles.
But one right angle
= 90~ = 100z = 2 radians.
Hence the required angle
= 144~ =160s= 4 radians.
EXAMPLES. III.
Express in degrees, minutes, and seconds the angles,
7To 4rc
1. -. 2. 3' 3. 10rC. 4. 1. 5. 8c.
Express in grades, minutes, and seconds the angles,
4WC 77rC
6. 5 7. 6 8. 10rc.
Express in radians the following angles:
9. 60~. 10. 110~ 30'. 11. 1750 45'. 12. 47~ 25'36".
13. 395~. 14. 60g. 15. 110930'. 16. 345925 36'.