Some Applications of Trigonometry Class 10 Notes Maths Chapter 9

Terminologies related to Heights and Distances

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.

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.

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.

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.

How to convert the above figure into the right triangle.

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)

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)

• 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:

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

Trick to remember Trigonometric Ratios
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