This document discusses trigonometry and its applications. It defines trigonometry as the measurement of triangles and angles, and notes its Greek roots. Some key applications are mentioned like surveying, navigation, physics and engineering. It defines angle of elevation and depression. It then provides an example problem to find the distance between two ships based on the observed angle of elevation of a lighthouse from each ship.

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

3. The word
‘trigonometry’ is
We derived from the In
make Greek word ‘tri’ trigo. in
use of meaning three , ‘gon’ daily life
meaning sides and we make use
trigonometry of the angles of
to measure the ‘metron’ meaning
measures. sine ratio, cosine
height and ratio and tangent
distance with our ratios. We make use
eye contact only. of angles 30 , 45 ,
60 and 90 and the
We do not use the values given to
measuring tapes. them.

4. 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.

5. 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.

6. 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.
Horizontal level

7. 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

14. Q: Two ships are sailing in ANS :
• AB = 100 m, ACB = 30º and ADB = 45º
the sea on the two sides of •AB/AC = tan 30º = 1/3 AC = AB x
a lighthouse. The angle of B 3 = 100 3 m
elevation of the top of the • AB/AD = tan 45º = 1 AD = AB
lighthouse is observed = 100 m
from the ships are 30º and • CD = (AC + AD)= (100 3 +
100) m
45º respectively. If the = 100(3 + 1)
100 m
lighthouse is 100 m high, = (100 x 2.73) m
find the distance between = 273 m
the two ships .
30º 45º
C A D