\fdO'^ - Old Forge Coal Mines

154 GEOMETRY AND TRIGONOMETRY.
draw the lines C D and C B perpendicular, respectively,
If
to the radii O E and O A. C B is, the
sine, C D the cosine, and A T the tan-
gent.
(317) Suppose that in Fig. 10, the
line A T has been drawn equal to 3
times the radius O A. From T draw
T O; then, the tangent
TA
OA
oi T O A
= 3. Where T O cuts the circle
at C, draw CD and C B perpendicu-
lar, respectively,
\.o O E and O A.
C D vs, the cosine and C B the sine.
Fig. 10. The angle corresponding to tan 3 is
/ound by the table to equal 71° 33' 54"; therefore, sin
71° 33' 54" = .94868 and cos 71° 33' 54" = .31623.
(318) The angle whose cos is .39278 = 66° 52' 20'.
Sin of 66° 52' 20" = .91963.
Tan of 66° 52' 20" = 2.34132.
3
For a circle with a diameter 4— times as large, the values
of the above cos, sin, and tan will be
.3
.39278= 1.86570 cos.
.91963= 4.36824 sin.
C- X 2.34132 = 11.12127 tan-
4
>- Ans.
(319) See Fig. 11. Angle B = 180° - (29° 21'
+ 76° 44' 18") = 180° - 106° 5' 18" = 73° 54' 42".
From C^ draw C D perpendicular
to A B.
A D = A C cos A = 31.833
X cos 29° 21' = 31.833 X .87164
= 27.747 it. CD = A C sin A
= 31.833 X sin 29° 21' = 31.833
X .49014 = 15.603. fig. 11.