Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, such as of trees, towers, water tanks, and distance from a ship to a lighthouse. It provides examples of using trigonometry to calculate the height of a tower given the angle of elevation and distance from its base, and the height of a pole given the angle made by the rope tied to its top and the ground.

1. TRIGONOMETRY
&
ITS APPLICATION
S.KISHORE KUMAR, M.Sc., B.Ed., MBA
MATHEMATICS (TGT)
GMR V DAV PUBLIC SCHOOL,RAJAM

6. What is Trignometry?Trigonometry is a branch
of mathematics that studies triangles and
the relationships between their sides and
the angles between these sides.
In this topic we shall make use of
Trignometric Ratios to find the
height of a tree,a tower,a water
tank,width of a river,distance of
ship from lighthouse etc.
Line of SightHorizontalAngle of Elevation
The angle which the line of sight
makes with a horizontal line drawn
away from their eyes is called the
angle of Elevation of aeroplane from
them.
Angel of ElevationAngel of ElevationAngel of Depression
If the pilot of the aeroplane looks
downwards at any object on the
ground then the Angle between his
line of sight and horizontal line
drawn away from his eyes is called
Angel of Depression
Angle of DepressionHorizontalAngel of Depression
Now let us Solve some
problem related to
Height and Distance
The angle of elevation of the top of a tower from a
point on the ground, which is 30 m away from the
foot of the tower is 30°. Find the height of the tower.
.
Let AB be the tower and the angle of elevation from point C
(on ground) is
30°.
In ΔABC,
Therefore, the height of the tower is
A circus artist is climbing a 20 m long rope, which is tightly
stretched and tied from the top of a vertical pole to the
ground. Find the height of the pole, if the angle made by the
rope with the ground level is 30 °.
Sol:- It can be observed from the figure that AB is the pole.
In ΔABC,
Therefore, the height of the pole is 10 m..
Let K be the kite and the string is tied to point P on
the ground.
In ΔKLP,
Hence, the length of the string is,.Height of tree =+ BCHence, the height of the tree is