Plane trigonometry, by S.L. Loney.

46

TRIGONOMETRY.

[Exs. VIII.]

16. Two flagstaffs stand on a horizontal plane. A and B are two
points on the line joining the bases of the flagstaffs and between them.
The angles of elevation of the tops of the flagstaffs as seen from A are
30~ and 60~ and, as seen from B, they are 60~ and 45~. If the length AB
be 30 feet, find the heights of the flagstaffs and the distance between
them.
17. P is the top and Q the foot of a tower standing on a horizontal
plane. A and B are two, points on this plane such that AB is.32 feet and QAB is a right angle. It is found that cot PAQ- and
cot PBQ=3;
find the height of the tower.
18. A square tower stands upon a horizontal plane. From a point
in this plane from which three of its upper corners are visible their
angular elevations are respectively 45~, 60~, and 45~. Shew that the
height of the tower is to the breadth of one of its sides as,/6 (/5 + 1)
to 4.
19. A lighthouse, facing north, sends out a fan-shaped beam of
light extending from north-east to north-west. A steamer sailing due
west first sees the lighthouse when it is 5 miles away from the lighthouse
and continues to see it for 30V/2 minutes. What is the speed of the
steamer?
20. A man stands at a point X on the bank XY of a river with
straight and parallel banks and observes that the line joining X to a
point Z on the opposite bank makes an angle of 30~ with XY. He then.goes along the bank a distance of 200 yards to Y and finds that the angle
ZYX is 60~. Find the breadth of the river.
21. A man, walking due north, observes that the elevation of a
balloon, which is due east of him and is sailing toward the north-west,
is then 60~; after he has walked 400 yards the balloon is vertically over
his head; find its height supposing it to have always remained the same.