Application
of Trigonometry
1 1.
The line drawn from the eye of an
observer to a point in the object where the person is viewing is called -
a)
horizontal line b) line of sight
c) vertical
line d)
parallel line
2 The angle formed by the line of sight
with the horizontal line when the object is above the horizontal level is
called the -
a) angle of
elevation b) angle of depression
c) alternate angle d) vertical opposite angle
3. The angle formed by the line of sight
with the horizontal when the object is below the horizontal level is called --
a) angle of elevation b)
angle of depression c) alternate angle d) vertical
opposite angle
4 .
A ladder is 100√3
m high. Find the angle of elevation of its top from a point 100m away from its
foot. a) 300 b) 450 c)
600 d)
900
5.
A ladder makes an angle of 60 deg.
with the ground when placed against a wall. If the foot of the ladder is 2m
away from the wall, then the length of the ladder is- a) 4m b) 4√3
m c) 4/√3m d)
6m
6.
The ratio of the length of a rod and
its shadow is 1 : √3. What is the angle of elevation of the sun? a)
300 b) 450 c)
600 d) 900
7.
If the angles of elevation of the top
a tower from two points distant a and b from the base and in the same straight
line with it are complementary then the height of the tower is -
a)
ab b)
a√b c) a/√3m d)a
8.
If the angles of elevation of the top
a tower from two points distant 4m and 9m from the base and in the same
straight line with it are complementary then the height of the tower is -
a)
4m b) 6m c)
9m d) 12m
9.
The angle of depression of a car
parked on the road from the top of a 150m high tower is 300. The
distance of the car from the tower is -
a)
50m b)50√3m c) 150√2m d) 100m
10. From
a light house the angle of depression of two ships on opposite sides of the
light house are observed to be 300 and 450. If the height
of the light house is h metres, what is the distance between the ships?
A)
(√3 + 1)m b) (√3
– 1)m c) √3
m d) 24m
11. A
kite is flying at a height of 60m above the ground. The string attached to kite
is temporarily tied to a point on the ground. The inclination of the string
with the ground is 60 deg. find the length of the string assuming that there is
no slack in the string?
a)40m b) 60√3m c) 60m d)
40√3m
12. A
tree 12m high is broken by the wind in such a way that its top touches the
ground and makes an angle of 60 deg. with the ground. At what height from the
bottom the tree is broken?
A)
5m b) 5.569m c)
6m d) 6.5m
13. When
we raise our hand to look at the object, the angle formed by the line of sight
with horizontal is known as -
a)
angle of elevation b)
angle of depression
c) acute
angle d)
obtuse angle
14. When the length of the shadow of a pillar is
equal to its height, the elevation at source of sight is -
a)
300 b) 450 c) 600 d) 900
15. A
ladder is 10m long. It touches a wall at height of 5m. the angle
made by it with
the horizontal line is -
a)
300 b) 450 c) 600 d) 900
16. The
tops of two poles of height 10m and 18m are connected with wire. If wire makes
an angle of 300 with horizontal, then length of wire is -
a)
10m b) 12m c)
16m d) 18m
17. A
ladder leans against wall at point B (window end) from a ground level and makes
an angle horizontally at 52°. height of ladder is 15 m. When same ladder leans
above point B at point A (window start) and makes an angle of 85° horizontally.
distance between point A and point B is-
a)
12.4m b) 3.12m c)
4m d) 5m
1 18. Height
of a light house is 65 m. angles of elevation and depression of top and foot of
a radar mast are 52° and 30° respectively. height of radar mast is -
a) 109m b) 209m c) 109.9m d) 209.9m
1 19. A
tower subtends an angle of 30 deg. at a point on the same level as its foot. At
a second point h meters above the first, the depression of the foot of the
tower is 60 degree. What is the height of the tower?
a)h
meter b)
h/2 meter c) h/3 meter d) h/4 meter
20. The
angle of elevation of a cloud from a point h metre above a lake is
The angle of depression of its reflection in the lake
is 45 degree. What is the height of cloud?
a)
h tan(45 + a)
c c)
h tan(45 - a)
Dr Rajesh Kumar Thakur
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