Plane trigonometry, by S.L. Loney.

DIP OF THE HORIZON. 269
Hence h2 is very small compared with hr.
As a close approximation we have then
OT = V2hr.
The dip =z TOQ
=90 - z COT= zOCT.
OT V2ahr /2h
Also tan OCT = =-T - r
so that, very approximately, we have the angle
OCT 2= / - radians
r
/2h 180~ [180 x 60 x 60 2h
236. Ex. Taking the radius of the earth as 4000 miles, find the dip
at the top of a lighthouse which is 264 feet above the sea and the distance
of the offing.
Here r=4000 miles, and 7h= 264 feet =- mile.
Hence h is very small compared with r, so that
OT= /- x 4000= 140 = 20 miles.
Also the dip = / radians = radian
'V r' 200
( x 1- 8 6 = ( )- = 17' 11" nearly.
EXAMPLES. XLII.
1. Find in degrees, minutes, and seconds the dip of the horizon from
the top of a mountain 4400 feet high, the earth's radius being 21 x 106
feet.
2. The lamp of a lighthouse is 196 feet high; how far off can it be
seen?