some applications of trigonometry

SomeApplications

Of Trigonometry

CONTENTS• Introduction• Applications of Trigonometry• Line of Sight• Angle of Elevation and Depression• Heights Around the World• Sample Problem

INTRODUCTION

The word ‘trigonometry’ is derived from the Greek word

‘tri’ meaning three , ‘gon’

meaning sides and ‘metron’

meaning measures.

We make use of trigonometry to measure the height and distance with our eye contact only. We do not use the measuring tapes.

In trigo. in daily life

we make use of the angles of

 sine ratio, cosine ratio and

tangent ratios. We make use of angles 30°, 45°, 60° and 90° and

thevalues given to

them.

Applications of

• Surveying• Navigation• Physics• Engineering• Finding the distance to the moon• Constructing sundials to estimate the time from the sun’s shadow.• Finding the height of a mountain/hill.

Line o

f

Sight

The line of sight is a straight line along which an observer observes an object. It is an imaginary line that stretches between observer's eye and the object that he is looking at.

Angle o

f

Elevatio

n

If the object being observed is above the horizontal, then the angle between the line of sight and the horizontal is called angle of elevation.

Line of

Sight

Horizontal level

Angle of Depressio

n

If the object being observed is below the horizontal, then the angle between the line of sight and the horizontal is called angle of depression.

Horizontal level

Line of Sight

HEIGHTS AROUND

THE WORLD

BURJ KHALIFA - DUBAI

HEIGHT :830m

Taipei 101-Taipei, TAIWAN

HEIGHT : 509M

Shanghai World

Financial Centre

HEIGHT :492M

WILLIS TOWER

- CHICAGO

Height :442m

EIFFEL TOWER-PARIS, FRANCE

HEIGHT : 324M

Q: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, find the distance between the two ships .

10

0

m30º 45º

A

B

C D

ANS : •  AB = 100 m, ACB = 30º and ADB

= 45º• AB/AC = tan 30º = 1/3

AC = AB x 3  = 100 3  m• AB/AD =  tan 45º = 1   AD

= AB = 100

m •  CD = (AC + AD)= (100

3  + 100) m

= 100(3  + 1)

= (100 x 2.73) m

= 273 m

SAMPLE PROBLEM