This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope attached to the top of the pole and the ground.

2. What is Trignometry?
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
Trignometric 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. Angle 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.

7. Angel of Elevation
Angel of Elevation

8. Angel 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

9. Angle of Depression
Horizontal
Angel of Depression

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

12. 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

13. 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.

14. 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

15. ,

16. Height of tree =
.
+ BC
Hence, the height of the tree is