Plane trigonometry, by S.L. Loney.

18

TRIGONOMETRY.

[Exs. IV.]

11. If the circumference of a circle be divided into 5 parts which are
in A. P., and if the greatest part be 6 times the least, find in radians
the magnitudes of the angles that the parts subtend at the centre of the
circle.
12. The perimeter of a certain sector of a circle is equal to the length
of the arc of a semicircle having the same radius; express the angle of
the sector in degrees, minutes, and seconds.
13. At what distance does a man, whose height is 6 feet, subtend an
angle of 10'?
14. Find the length which at a distance of one mile will subtend
an angle of 1' at the eye.
15. Find approximately the distance at which a globe, 52 inches in
diameter, will subtend an angle of 6'.
16. Find approximately the distance of a tower whose height is
51 feet and which subtends at the eye an angle of 5r5/'.
17. A church spire, whose height is known to be 45 feet, subtends
an angle of 9' at the eye; find approximately its distance.
18. Find approximately in minutes the inclination to the horizon of
an incline which rises 31 feet in 210 yards.
19. The radius of the earth being taken to be 3960 miles, and the
distance of the moon from the earth being 60 times the radius of the
earth, find approximately the radius of the moon which subtends at the
earth an angle of 16'.
20. When the moon is setting at any given place the angle that is
subtended at its centre by the radius of the earth passing through the given
place is 57'. If the earth's radius be 3960 miles, find approximately the
distance of the moon.
21. Prove that the distance of the sun is about 81 million geographical miles, assuming that the angle which the earth's radius
subtends at the distance of the sun is 8'76", and that a geographical
mile subtends 1' at the earth's centre. Find also the circumference and
diameter of the earth in geographical miles.
22. The radius of the earth's orbit, which is about 92700000 miles,
subtends at the star Sirius an angle of about '4"; find roughly the
distance of Sirius.