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Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

1. Line of Sight

When an observer looks from a point E (eye) at object O then the straight line EO between eye E and object O is called the line of sight.
Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

2. Horizontal Line

When an observer looks from a point E (eye) to another point Q which is horizontal to E, then the straight line, EQ between E and Q is called the horizontal line.
Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

3. Angle of Elevation

When the eye is below the object, then the observer has to look up from point E to object O. The measure of this rotation (angle θ) from the horizontal line is called the angle of elevation.
Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

4. Angle of Depression

When the eye is above the object, then the observer has to look down from point E to the object. The horizontal line is now parallel to the ground. The measure of this rotation (angle θ) from the horizontal line is called the angle of depression.

Some Applications of Trigonometry Class 10 Notes Maths Chapter 9
How to convert the above figure into the right triangle.


Question for Short Notes: Some Application of Trigonometry
Try yourself:What is the term for the measure of the rotation angle (θ) from the horizontal line when an observer looks down from a point E to an object O?
View Solution

Case I: Angle of Elevation is known

Draw OX perpendicular to EQ.

Now ∠OXE = 90°

ΔOXE is a rt. Δ, where

OE = hypotenuse

OX = opposite side (Perpendicular)

EX = adjacent side (Base)

Some Applications of Trigonometry Class 10 Notes Maths Chapter 9


Case II: Angle of Depression is known

(i) Draw OQ’parallel to EQ

(ii) Draw perpendicular EX on OQ’.

(iii) Now ∠QEO = ∠EOX = Interior alternate angles

ΔEXO is an rt. Δ. where

EO = hypotenuse

OX = adjacent side (base)

EX = opposite side (Perpendicular)

Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

  • Choose a trigonometric ratio in such a way that it considers the known side and the side that you wish to calculate.
  • The eye is always considered at ground level unless the problem specifically gives the height of the observer.
  • The object is always considered a point.

Example: The angle of elevation of a cloud from a point 60 m above a lake is 

30 degrees and the angle of depression of the reflection of cloud in the lake is 

60 degrees. Find the height of the cloud.

Sol:

Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

In ΔABE, we have

tan30 = h/x

1/√3 = h/x

⇒x=h√3

In ΔBDE, we have

tan60 = (120+h)/h√3

⇒√3 = (120 + h)/h√3

⇒3h = 120 + h

⇒2h=120

⇒h=60 m

Hence, height of cloud above the lake = 60+h=60+60=120m

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Some Applications of Trigonometry Class 10 Notes Maths Chapter 9
The document Some Applications of Trigonometry Class 10 Notes Maths Chapter 9 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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