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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 Applications 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
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FAQs on Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

1. What is the angle of elevation in trigonometry?
Ans. The angle of elevation is the angle formed by the horizontal line and the line of sight when looking up at an object above the horizontal level. It is used in solving problems related to heights and distances.
2. How is the angle of depression defined?
Ans. The angle of depression is the angle formed by the horizontal line and the line of sight when looking down at an object below the horizontal level. This concept is important when calculating the height of objects based on their distance from the observer.
3. What trigonometric ratios are commonly used in height and distance problems?
Ans. The commonly used trigonometric ratios in height and distance problems are sine, cosine, and tangent. These ratios relate the angles to the ratios of the lengths of the sides of right-angled triangles.
4. Can you explain a real-life application of the angle of elevation?
Ans. One real-life application of the angle of elevation is in determining the height of a building. By measuring the distance from a point to the base of the building and the angle of elevation to the top of the building, one can use trigonometry to calculate its height.
5. How do you solve problems involving angles of elevation and depression?
Ans. To solve problems involving angles of elevation and depression, first, identify the right triangle formed by the observer, the object, and the horizontal line. Then, use the appropriate trigonometric ratios (tangent, sine, or cosine) based on the known measurements to find the unknown lengths, such as height or distance.
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