This document discusses applications of trigonometry, including determining the height or length of objects using angles of elevation/depression and trigonometric ratios. It provides examples like calculating the height of a pole given the observation angle and distance, or finding the width of a river based on the boat's angle and distance traveled. The document ends with 20 multiple choice questions testing these trigonometric application concepts.

1. 12. Applications
of Trigonometry

2. 12. Applications of Trigonometry
Page 2
12.Applications of trigonometry
 The line of sight is the line drawn from the eye of an observer to a point on the
object being viewed by the observer.
 The angle of elevation of the object viewed, is the angle formed by the line of
sight with the horizontal when it is above the horizontal level, i.e., the case when
we raise our head to look at the object.
 The angle of depression of an object viewed, is the angle formed by the line of
sight with the horizontal when it is below the horizontal level, i.e., the case when
we lower our head to look at the object.
 The height or length of the distance between two or distant objects can be
determined with the help of trigonometric ratios.
Multiple Choice Questions
1. A boy observed the top of an electric pole at an angle of elevation of
when the observation point is 8m from the foot of the pole then the height of
the pole is
(a) (b) (c) (d)
2. Rajender observes a person standing on the ground from a helicopter at
angle of depression . If the helicopter flies at a height of 50m from the
ground, then the distance of the person from Rajender.
(a) (b) (c) (d) None
3. Length of the shadow of a 15m high pole is m at 7 o clock in the morning.
Then what is the angle of elevation of the sun rays with the ground at the
time ?
(a) (b) (c) (d)
4. The ratio of the length of a rod and its shadow is . The angle of elevation
of the sun is
(a) (b) (c) (d)
5. If the angle of elevation of a tower from a distance of 100m from its foot is
then the height of the tower is
(a)100 (b) (c) (d)

3. 12. Applications of Trigonometry
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6. If the altitude of the sun is at then the height of the vertical tower that
will cast a shadow of length, 30m is
(a)30 (b) (c) (d)
7. A statue stands on the top of a 2m tall pedestal. From a point on the ground,
the angle of elevation of the top of the statue is and from the same point,
the angle of elevation of the top of the pedestal is Then the height of the
statue
(a) (b)1.3 (c) (d)
8. From the top of a building, the angle of elevation of the top of a cell tower is
and the angle of depression to its foot is If distance of the building
from the tower is 7m, then the height of the tower is
(a) (b)18 (c) (d)
9. A wire of length 18m had been tied with an electric pole at angle of elevation
with the ground. As it is covering a long distance, it was cut and tied at
angle of elevation with the ground. Then the length of the wire that has
to cut
(a) (b)7.6 (c) (d)
10. The angles of elevation of the top of a tower from two points at a distance of
4m and 9m, then the height of the tower from the base of the tower and in the
same straight line with it are complementary
(a)8 (b)7 (c)6 (d)5
11. From a light house the angles of depression of two ships on opposite sides of
the light house are observed to be and . If the height of the light
house is meters . Then the distance between the ship is
(a) (b)
(c) (d)
12. The tops of two poles of height 20m and 14m are connected by a wire. If the
wire makes an angle of with the horizontal, then the length of the wire is
(a)12 (b)10 (c)8 (d)6
13. From the top of a cliff 25m high the angle of elevation of a tower is found to
be equal to the angle of depression of the foot of the tower. The height of the
tower is
(a)25 (b)5 (c)75 (d)100

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14. If the angle of elevation of a cloud from a point 200m above the lake is
and the angle of depression of its reflection in the lake is , then the height
of the cloud above lake, is
(a)200 (b)5 (c)300 (d)None
15. The height of a tower is 100m. When the angle of elevation of the sun
changes from from , the shadow of the tower becomes meters less.
The value of is
(a)100 (b) (c) (d)
16. Two persons are a meter apart and the height of one is double that of the
other. If from the middle point of the line joining their feet, an observer finds
the angular elevation of their tops to be complementary, then the height of
the shorter person is
(a) (b) (c) (d)
17. A tree breaks due to storm and the broken pat bends so that the top of the
tree touches the ground by making angle with the ground. The istance
between the foot of the tree and the top of the tree on the ground is m. then
the height of the tree before falling down.
(a) (b) (c) (d)
18. Two men on either side of a temple of 30 meters high observe its top at the
angles of elevation and respectively. Then the distance between the
two men is
(a)20 (b) (c) (d)
19. An observer of height 1.8m is 13.2m away from a palm tree. The angle of
elevation of the top of the tree from his eyes is . Then the height of the
palm tree is
(a)16 (b)14 (c)15m (d)13
20. A boat has to cross a river. It crosses the river by making an angle of with
the bank of the river due to the stream of the river and travels a distance of
600m to reach the another side of the river. Then the width of the river is
(a)600 (b)800 (c)400m (d)None

5. 12. Applications of Trigonometry
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Answers
1 2 3 4 5 6 7 8 9 10
c a c a b a a c b c
11 12 13 14 15 16 17 18 19 20
a a b d c d a b c b