Plane trigonometry, by S.L. Loney.

HEIGHTS AND DISTANCES.

213

To facilitate the statement of the bearing of a point
the circumference of the mariner's compass-card is divided
into 32 equal portions, as in the above figure, and the subdivisions marked as indicated. Consider only the quadrant
between East and North. The middle point of the arc
between N. and E. is marked North-East (N.E.). The
bisectors of the arcs between N.E. and N. and E. are
respectively called North-North-East and East-NorthEast (N.N.E. and E.N.E.). The other four subdivisions,
reckoning from N., are called North by East, N.E. by
North, N.E. by East, and East by North. Similarly the
other three quadrants are subdivided.
It is clear that the arc between two subdivisions of
360~
the card subtends an angle of -360 i.e. 11~, at the
centre 0.
EXAMPLES. XXXIII.
1. A flagstaff stands on the middle of a square tower. A man on
the ground opposite the middle of one face and distant from it 100 feet
just sees the flag; receding another 100 feet the tangents of elevation of
the top of the tower and the top of the flagstaff are found to be 2
and. Find the dimensions of the wer ad the height of the agstaff,
and 9. Find the dimensions of the tower and the height of the flagstaff,
the ground being horizontal.
2. A man, walking on a level plane towards a tower, observes that
at a certain point the angular height of the tower is 10~ and after going
50 yards nearer the tower the elevation is found to be 15~. Having given
L sin 15~=9 4129962, L cos 5 = 99983442,
log 25-783 = 14113334 and log 25-784= 1-4113503,
find, to 4 places of decimals, the height of the tower in yards.