Plane trigonometry, by S.L. Loney.

MEASUREMENT OF ANY ANGLE IN RADIANS.

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In the second case the height y is given by
Y - =number of radians in 5'
440 x3
1 7r
12 x 180'
11 11 22
so that y= 1 7r==-_ x - feet nearly
18 18 7
=about 23 inches.
EXAMPLES. IV.
1. Find the number of degrees subtended at the centre of a circle by
an arc whose length is -357 times the radius, taking 7r=3'1416.
2. Express in radians and degrees the angle subtended at the centre
of a circle by an arc whose length is 15 feet, the radius of the circle
being 25 feet.
3. The value of the divisions on the outer rim of a graduated circle
is 5' and the distance between successive graduations is '1 inch. Find
the radius of the circle.
4. The diameter of a graduated circle is 6 feet and the graduations
on its rim are 5' apart; find the distance from one graduation to
another.
5. Find the radius of a globe which is such that the distance between
two places on the same meridian whose latitude differs by 1~ 10' may be
half-an-inch.
6. Taking the radius of the earth as 4000 miles find the difference
in latitude of two places, one of which is 100 miles north of the other.
7. Assuming the earth to be a sphere and the distance between
two parallels of latitude, which subtends an angle of 1~ at the earth's
centre, to be 691 miles, find the radius of the earth.
8. The radius of a certain circle is 3 feet; find approximately the
length of an arc of this circle, if the length of the chord of the arc be
3 feet also.
9. What is the ratio of the radii of two circles at the centre of which
two arcs of the same length subtend angles of 60~ and 75~?
10. If an arc, of length 10 feet, on a circle of 8 feet diameter
subtend at the centre an angle of 143~ 14'22"; find the value of r
to 4 places of decimals.

L. T.

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