Plane trigonometry, by S.L. Loney.

16

TRIGONOMETRY.

Ex. 8. Assuming the average distance of the earth from the sun to be
92500000 miles, and the angle subtended by the sun at the eye of a person
on the earth to be 32', find the sun's diameter.
Let D be the diameter of the sun in miles.
The angle subtended by the sun being very small, its diameter is very
approximately equal to a small arc of a circle whose centre is the eye of
the observer. Also the sun subtends an angle of 32' at the centre of this
circle.
Hence, by Art. 21, we have
D
_ = the number of radians in 32'
92500000
8~
=the number of radians in -
15
8 7r 27r
15 180 675'
185000000
'D- =r miles
675
185000000 22
-= 75 x - miles approximately
- 675 7
= about 862000 miles.
Ex. 4. Assuming that a person of normal sight can read print at such
a distance that the letters subtend an angle of 5' at his eye, find what is
the height of the letters that he can read at a distance (1) of 12 feet, and
(2) of a quarter of a mile.
Let x be the required height in feet.
In the first case, x is very nearly equal to the arc of a circle, of radius
12 feet, which subtends an angle of 5' at its centre.
Hence = number of radians in 5'
12
1 7r
12 ^ 1i80'
r 1 22
x = 1 feet = - x feet nearly
180 180 7
1 22 1
= x - inches=about - inch.
iu 7 5