CHAPTER – APPLICATIONS OF TRIGONOMETRY
Key Concepts:
1. Angle of Elevation:
o The angle of elevation is the angle between the horizontal line and the line of
sight when looking up at an object.
o It is used to find the height of an object from a certain distance.
2. Angle of Depression:
o The angle of depression is the angle between the horizontal line and the line of
sight when looking down at an object.
o It helps in finding the distance to an object when the height is known.
1. The height of a tower is 10 m. What is the length of its shadow when Sun’s
altitude is 45°?
(a) 10 m (b) 30 m (c) 20 m (d) none of these
2. If the ratio of the height of a tower and the length of its shadow is √3 ∶ 1,
what is the angle of
elevation of the sun?
(a) 30° (b) 60° (c) 45° (d) none of these
3. What is the angle of elevation of the Sun when the length of the shadow of a
vertical pole is
equal to its height?
(a) 30° (b) 0° (c) 45° (d) none of these
4. A tower is 50 m high, its shadow is ‘x’ metres shorter when the sun’s altitude
is 45° than when
it is 30°. Find the value of ‘x’.
(a) 100√3 m (b) 200
√3
m (c) 50√3m (d) none of these
5. _____________ is the line drawn from the eye of an observer to the point in the
object viewed
by the observer.
6. The ____________ of an 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.
7. The ____________ 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.
8. Assertion : When we move towards the object, angle of elevation decreases.
Reason: As we move towards the object, it subtends large angle at our eye than
before.
9. Assertion : At some time of the day, the length of the shadow of a tower is
equal to
its height, then the sun’s altitude is 45°.
Reason : The angle which the line of sight makes with the horizontal line passing
through the
eye of the observer, when the object is above the observer is called
the angle of elevation.
10. A boat is being rowed away from a cliff 150m high. At the top of the cliff the
angle of
depression of the cliff changes from 600 to 450 in 2 minutes. Find the speed of the
boat.
11. At a point on level ground, the angle of elevation of a vertical tower is found
to be such that its
Key Concepts:
1. Angle of Elevation:
o The angle of elevation is the angle between the horizontal line and the line of
sight when looking up at an object.
o It is used to find the height of an object from a certain distance.
2. Angle of Depression:
o The angle of depression is the angle between the horizontal line and the line of
sight when looking down at an object.
o It helps in finding the distance to an object when the height is known.
1. The height of a tower is 10 m. What is the length of its shadow when Sun’s
altitude is 45°?
(a) 10 m (b) 30 m (c) 20 m (d) none of these
2. If the ratio of the height of a tower and the length of its shadow is √3 ∶ 1,
what is the angle of
elevation of the sun?
(a) 30° (b) 60° (c) 45° (d) none of these
3. What is the angle of elevation of the Sun when the length of the shadow of a
vertical pole is
equal to its height?
(a) 30° (b) 0° (c) 45° (d) none of these
4. A tower is 50 m high, its shadow is ‘x’ metres shorter when the sun’s altitude
is 45° than when
it is 30°. Find the value of ‘x’.
(a) 100√3 m (b) 200
√3
m (c) 50√3m (d) none of these
5. _____________ is the line drawn from the eye of an observer to the point in the
object viewed
by the observer.
6. The ____________ of an 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.
7. The ____________ 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.
8. Assertion : When we move towards the object, angle of elevation decreases.
Reason: As we move towards the object, it subtends large angle at our eye than
before.
9. Assertion : At some time of the day, the length of the shadow of a tower is
equal to
its height, then the sun’s altitude is 45°.
Reason : The angle which the line of sight makes with the horizontal line passing
through the
eye of the observer, when the object is above the observer is called
the angle of elevation.
10. A boat is being rowed away from a cliff 150m high. At the top of the cliff the
angle of
depression of the cliff changes from 600 to 450 in 2 minutes. Find the speed of the
boat.
11. At a point on level ground, the angle of elevation of a vertical tower is found
to be such that its
