21. A man P walking towards a building AB finds that the building disappears
from his view when the angle of elevation of the top C of a wall is x°, where
tan x° = 1/3. The wall is 1.8 m high, and the distance between the wall and
the building is 3.6 m. Find the height of the building.
22. A vertical tower subtends a right angle at the top of a vertical flag on the
ground, the height of the flag being 10 m .If the distance between the tower
and the flag be 20 m, find the height of the tower.
23. A vertical pole on one side of a street subtends a right angle at the top of
a lamp post exactly on the opposite side of the street. If the angle of
elevation of the top of the lamp post from the base of the pole is 58° 30’ and
the width of the street is 30 m, find the heights of the pole and the lamp
post.
24. From the top of a hill 200 m height, the angles of depression of the top
and the bottom of a pillar are 45° and 59° 36’respectively. Find the height of
the pillar and its distance from the hill.
25. A bird is perched on the top of a tree 20 m high and its angle of
elevation from a point on the ground is 45°. The bird flies off horizontally
straight away from the observer and in 1 sec the angle of elevation of the
bird reduces to 35°. Find the speed of the bird.
26. The angles of depression and elevation of top of 12 m high wall from the
top and the bottom of a tree are 60° and 30° respectively. Find
(i) the height of the tree, and
(ii) the distance of the tree from the wall.
27. Two pillars of equal height stand on either side of a road which is 40 m
wide. From a point on the road between the pillars, the angles of elevation of
tops of the pillars are 30° and 60°. Find
(i) the position of the point of the point on the road, and
(ii) the height of each pillar.
28. A ladder rests against a house on one side of a street. The angle of
elevation of the top of the ladder is 60°. The ladder is turned over to rest
against a house. On the other side of the street and the elevation now
becomes 42° 50’. If the ladder is 40 m long, find the breadth of the street.
29. The angle of elevation of a cloud from a point h metre above a lake is
30° and the angle of depression of its reflection is 45°. If the height of the
cloud be 200 metres, Find h.
Answers
A man P walking towards a building AB finds that the building disappears
from his view when the angle of elevation of the top C of a wall is x°, where
tan x° = 1/3. The wall is 1.8 m high, and the distance between the wall and
the building is 3.6 m. Find the height of the building.
22. A vertical tower subtends a right angle at the top of a vertical flag on the
ground, the height of the flag being 10 m .If the distance between the tower
and the flag be 20 m, find the height of the tower.
23. A vertical pole on one side of a street subtends a right angle at the top of
a lamp post exactly on the opposite side of the street. If the angle of
elevation of the top of the lamp post from the base of the pole is 58° 30’ and
the width of the street is 30 m, find the heights of the pole and the lamp
post.
24. From the top of a hill 200 m height, the angles of depression of the top
and the bottom of a pillar are 45° and 59° 36’respectively. Find the height of
the pillar and its distance from the hill.
25. A bird is perched on the top of a tree 20 m high and its angle of
elevation from a point on the ground is 45°. The bird flies off horizontally
straight away from the observer and in 1 sec the angle of elevation of the
bird reduces to 35°. Find the speed of the bird.
26. The angles of depression and elevation of top of 12 m high wall from the
top and the bottom of a tree are 60° and 30° respectively. Find
(i) the height of the tree, and
(ii) the distance of the tree from the wall.
27. Two pillars of equal height stand on either side of a road which is 40 m
wide. From a point on the road between the pillars, the angles of elevation of
tops of the pillars are 30° and 60°. Find
(i) the position of the point of the point on the road, and
(ii) the height of each pillar.
28. A ladder rests against a house on one side of a street. The angle of
elevation of the top of the ladder is 60°. The ladder is turned over to rest
against a house. On the other side of the street and the elevation now
becomes 42° 50’. If the ladder is 40 m long, find the breadth of the street.
29. The angle of elevation of a cloud from a point h metre above a lake is
30° and the angle of depression of its reflection is 45°. If the height of the
cloud be 200 metres,
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