Angle of Elevation
&
Angle of Depression
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.
Object
Eye
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
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.
Solutions
12.6
tan  
58.5
 
12.6
  tan
58.5
1
 = angle of depression
  12.15º

12.6m
eye

Ground level
58.5m
object
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.
Sketch
Solution
tan   16.9
27.5
 
  tan 1 16.9
27.5
  31.57º
Angle of elevation of this person line of
sight is 31.57º
Angle of depression
Find the height of the man in the
hot air balloon from the ground.
= 50°
h =100 tan 50°
= 119.2m
h
100m
Exercise
FIND THE HEIGHT OF THE TOWER
Height of tower
= 53 tan 80°
= 300.6m
80º
53m
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?
Solution
Let x m be the distance of the object
from the base of the cliff.