This document discusses trigonometry and how it can be used to calculate heights and distances. It defines angle of elevation and depression, and provides examples of using trigonometric ratios to calculate the height of a tower, pole, and kite string based on observed angles of elevation or depression. Sample problems are worked through showing the application of trigonometric functions like tangent and sine to find unknown lengths.

1. Done By:
Name: Gourisankaran Pillai
Class: 10 E
School: Christ Nagar
Central School

2. Trigonometry is a branch of mathematics
that studies triangles and the relationships
between their sides and the angles between
these sides.

3. In this topic we shall make
use of Trigonometric Ratios to
find the height of a tree, a
tower, a water tank, width of
a river, distance of ship from
lighthouse etc.

5. Line of Sight
Horizontal

6. 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.

7. Angel of Elevation

8. 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 ‘Angle
of Depression.’

9. Angle of Depression
Horizontal
Angle of
Depression

11. Now let us Solve some
problem related to
Height and Distance

12. Sol:- 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 .

13. Sol:- It can be observed from the figure that AB is the pole.
In ΔABC,
Therefore, the height of the pole is 10 m.

14. .
Sol:- 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 .