Plane trigonometry, by S.L. Loney.

220

TRIGONOMETRY.

EXAMPLES. XXXIV.
1. A bridge has 5 equal spans, each of 100 feet measured from the
centre of the piers, and a boat is moored in a line with one of the middle
piers. The whole length of the bridge subtends a right angle as seen
from the boat. Prove that the distance of the boat from the bridge is
100,/6 feet.
2. A ladder placed at an angle of 75~ just reaches the sill of a
window at a height of 27 feet above the ground on one side of a street.
On turning the ladder over without moving its foot, it is found that
when it rests against a wall on the other side of the street it is at an
angle of 15~ with the ground. Prove that the breadth of the street and
the length of the ladder are respectively
27 (3 + /3) and 27 (\/6 - /2) feet.
3. From a house on one side of a street observations are made of the
angle subtended by the height of the opposite house; from the level of
the street the angle subtended is the angle whose tangent is 3; from two
windows one above the other the angle subtended is found to be the
angle whose tangent is - 3; the height of the opposite house being
60 feet, find the height above the street of each of the two windows.
4. A rod of given length can turn in a vertical plane passing through
the sun, one end being fixed on the ground; find the longest shadow it
can cast on the ground.
Calculate the altitude of the sun when the longest shadow it can cast
is 3~ times the length of the rod.
5. A ship A observes another ship B leaving a harbour, whose
bearing is then N.W. After 10 minutes A, having sailed one mile N.E.,
sees B due west and the harbour then bears 60~ West of North. After
another 10 minutes B is observed to bear S.W. Find the distances
between A and B at the first observation and also the direction and rate
of B.
6. A ship sailing north sees two lighthouses, which are 6 miles
apart, in a line due west; after an hour's sailing one of them bears S.W.
and the other S.S.W. Find the ship's rate.