this is mathematics

1. Angle of Elevation
&
Angle of Depression

2. When a person looks at something
above his/her location, the angle
between the line of sight and the
horizontal is called the angle of
elevation. In this case, the line of sight
is "elevated" above the horizontal.
Eye
Object

3. When a person looks at something
below his or her location, the angle
between the line of sight and the
horizontal is called the angle of
depression. In this case, the line of
sight is "depressed" below the
horizontal.Eye
Object

4. A stands at the window of a
so that his are 12.6 m above the
level ground in the vicinity of the
An object is 58.5 m away from the
on a line directly beneath the
Find the angle of depression of the
person's line of sight to the object on the
ground.

5. Solutions
θ = angle of depression
12.6tan
58.5
θ =
eye
12.6m
Ground level
object
58.5m
Line of sight
θ
( )1 12.6tan
58.5
−
θ =
θ ≅ 12.15º
θ

6. Exercise
Calculate the angle of elevation of the
line of sight of a person whose eye is
1.7 m above the ground, and is looking
at the top of a tree which is 27.5 m away
on level ground and 18.6 m high.

7. Sketch

8. Solution
16.9tan
27.5
θ =
( )1 16.9tan
27.5
−
θ =
θ ≅ 31.57º
Angle of elevation of this person line of
sight is 31.57º

9. Angle of depression
100m
h
Find the height of the man in the
hot air balloon from the ground.
= 50°
h =100 tan 50°
= 119.2m

10. FIND THE HEIGHT OF THE TOWER
80º
53m
Exercise
Height of tower
= 53 tan 80°
= 300.6m

11. Exercise
From the top of a vertical cliff 40 m high,
the angle of depression of an object
that is level with the base of the cliff is
34º.
How far is the object from the base of
the cliff?

12. Solution
Let x m be the distance of the object
from the base of the cliff.