HEIGHT AND DISTANCE
1.
A pole was broken by
the storm of wind and its top struck the ground at an angle of 300
and at a distance of 20 m from the foot of the pole. The height of the pole
before it was broken was
(1) 20
m (2)
m (3)
60 m
(4) 
m
m (2)
m (3)
60 m
(4) m
2.
The length of a shadow
of a vertical tower is 
times its height. The angle of elevation of
the sun is
times its height. The angle of elevation of
the sun is
(1) 300 (2) 450 (3) 600 (4) 
900
900
3.
A tree is broken by
the wind. If the top of the tree struck the ground at an angle of 300
and at a distance of 30 m from the root, then the height of the tree is
(1) 25 m (2) 30 m (3) 15 m (4) 20 m
m (2) 30 m (3) 15 m (4) 20 m
4.
From the top of a
cliff 90 m high, the angles of depression of the top and bottom of a tower are
observed to be 300 and 600 respectively. The height of
the tower is
(1) 45m (2) 60m (3) 75m (4) 30m
30m
5.
There are two vertical
posts, one on each side of a road, just opposite to each other. One post is
108m high. From the top of this post, the angles of depression of the top and
foot of the other post are 300 and 600 respectively. The
height of the other post, in meter is
(1) 36
(2) 72 (3) 108 (4) 110
6.
Two poles of equal
heights are standing opposite to each other on either side of a road which is
100m wide. From a point between them on road, angles of elevation of their tops
are 300 and 600. The height of each pole in meter
(1) 25 (2) 20
(3) 28 (4) 
(2) 20 (3) 28 (4)
7.
A ladder is resting
against a wall at a height of 10m. If the ladder is inclined with the ground at
an angle of 300, then the distance of the foot of the ladder from
the wall is
(1) 
m (2) 
m (3) 10m (4) 20m
m (2) m (3) 10m (4) 20m
8.
A man 6ft tall casts a
shadow 4 ft long at the same time when a flag pole casts a shadow 50 ft long.
The height of the flag pole is
(1) 80 ft (2) 75
ft (3) 60 ft (4) 70 ft
9.
A vertical post 15 ft
high is broken at a certain height and its upper part, not completely separated
meets the ground at an angle of 300. Find the height at which the
post is broken
(1) 10 ft (2) 5
ft (3) 15(2 - ) ft (4) 5 ft
(2 - ) ft (4) 5 ft
10.
When the angle of
elevation of the sun increases from 300 to 600, the
shadow of a post is diminished by 5 m. Then the height of the post is
(1) 
m (2)
m (3)
m (4) 
m
m (2)
m (3)
m (4) m
11.
A man is climbing a
ladder which is inclined to the wall at an angle of 300. If he
ascends at a rate of 2 m/s, then he approaches the wall at the rate of
(1) 1.5 m/s (2) 1 m/s (3) 2 m/s (4) 2.5 m/s
12.
P and Q are two points
observed from the top of a building 10 m high. If the angles of depression of the
points are complementary and PQ = 20 m, then the distance of P from the
building is
m high. If the angles of depression of the
points are complementary and PQ = 20 m, then the distance of P from the
building is
(1) 25m (2) 45m (3) 30m (4) 40m
13.
At a point on a
horizontal line through the base of a monument, the angle of elevation of the
top of the monument is found to be such that its tangent is 
. On walking
138m towards the monument the secant of the angle of elevation is found to be 
. The height
of the monument (in m) is
. On walking
138m towards the monument the secant of the angle of elevation is found to be . The height
of the monument (in m) is
(1) 35
(2) 49
(3) 42 (4) 56
14.
The angles of
elevation of the top of a tower from two points A and B lying on the horizontal
through the foot of the tower are respectively 150 and 300.
If A and B are on the same side of the tower and AB = 48m, then the height of
the tower is
(1) 24 m
(2)
24 m (3) 24
m (4) 96 m
m
(2)
24 m (3) 24 m (4) 96 m
15.
From a point P on the
ground the angle of elevation of the top of a 10m tall building is 300.
A flag is hoisted at the top of the building and the angle of elevation of the
top of the flagstaff from P is 450. Find the length of the
flagstaff. (Take = 1.732)
= 1.732)
(1) 10(+2)m (2)
10(+1)m (3) 10 m (4) 7.32m
+2)m (2)
10(+1)m (3) 10 m (4) 7.32m
16.
The angle of elevation
of the top of a vertical tower situated perpendicularly on a plane is observed
as 600 from a point P on the same plane. From another point Q, 10m
vertically above the point P, the angle of depression of the foot of the tower
is 300. The height of the tower is
(1) 15 m (2) 30 m (3) 20 m (4) 25 m
17.
A vertical pole and a
vertical tower are standing on the same level ground. Height of the pole is
10m. From the top of the pole the angle of elevation of the top of the tower
and angle of depression of the foot of the tower are 600 and 300
respectively. The height of the tower is
(1) 20m (2)
30m (3) 40m (4) 50m
18.
From the top of a hill
200m high, the angle of depression of the top and the bottom of a tower are
observed to be 300 and 600 respectively. The height of
the tower is
(1) 
(2)
166
(3) 133
(4) 200
(2)
166 (3) 133 (4) 200
19.
From the top of a
tower of height 180m the angles of depression of two objects on either sides of
the tower are 300 and 450. Then the distance between the
objects are
(1) 180(3+)m (2) 180(3-)m (3) 180(
)m (4) 180(
)m
)m (2) 180(3-)m (3) 180()m (4) 180()m
20.
From an aeroplane just
over a straight road, the angles of depression of two consecutive kilometer
stones situated at opposite sides of the aeroplane were found to be 600
and 300 respectively. The height (in km) of the aeroplane from the
road at that instant, is
(1) 
(2) 
(3) 
(4) 
(2) (3) (4)
21.
The base of a triangle
is 12 cm and two angles at the base are 300
and 600 respectively. The altitude of the triangle is
cm and two angles at the base are 300
and 600 respectively. The altitude of the triangle is
(1) 12cm (2) 6cm (3) 10cm (4) 9cm
cm (4) 9cm
22.
A telegraph post is
bent at a point above the ground due to storm. Its top just touches the ground
at a distance of 10 m from its foot and makes an angle of 300
with the horizontal. Then height (in meters) of the of the telegraph post is
m from its foot and makes an angle of 300
with the horizontal. Then height (in meters) of the of the telegraph post is
(1) 30 (2) 24 (3) 20 (4) 25
23.
From two points on the
ground and lying on a straight line through the foot of a pillar, the two
angles of elevation of the top of the pillar, the two angles of elevation of
the top of the pillar are complementary to each other. If the distances of the
two points from the foot of the pillar are 12m and 27m and the two points lie
on the same side of the pillar, then the height (in meters) of the pillar is
(1) 12 (2) 18 (3) 15 (4) 16
24.
TF is a tower with F
on the ground. The angle of elevation of T from A is xo such that
tan xo = 
and AF = 200m. The angle of elevation of T
from a nearer point B is yo with BF = 80m. The value of yo
is
and AF = 200m. The angle of elevation of T
from a nearer point B is yo with BF = 80m. The value of yo
is
(1) 600 (2) 300 (3) 750 (4) 450
25.
The angle of
depression of a point situated at a distance of 70m from the base of a tower is
600. The height of the tower is
(1) 35m (2) 70m (3) 
m (4) 70m
m (2) 70m (3) m (4) 70m
26.
The ratio of the
length of a rod and its shadow is 1 : . The angle of
elevation of the sun is
. The angle of
elevation of the sun is
(1) 900 (2) 300 (3) 450 (4) 600
27.
A person of height
6ft. wants to pluck a fruit which is on a 
ft high tree.
If the person is standing 
ft. away from
the base of the tree, then at what angle should he throw a stone so that it
hits the fruit?
ft high tree.
If the person is standing ft. away from
the base of the tree, then at what angle should he throw a stone so that it
hits the fruit?
(1) 750 (2) 300 (3) 450 (4) 600
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