some applications of trigonometry
TRANSCRIPT
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