Angle of elevation is defined as the angle between the line of sight and the horizontal. By definition then, it assumes that you are looking at an object upwards, hence you form an angle of elevation with the horizontal.
Now let us look at some examples in angle of elevation:
Example 1: Tom looks at the top of a flag on a building which is 50m high from the ground. The angle of elevation to the top of the flag from the ground is 23°. How far away is Tom from the building?
tan 23° =
= 1117.79 m
So Tom is 117.79 m away from the building.
Example 2 : Brittany spots a bird on top of a tree at an angle of elevation of 40°. She is 50 m from the base of the tree. What is the height from the ground to the point where the bird is at the top of the tree?
tan 40° =
h = 50 tan 40°
= 41.95 m
The height at which the bird is found on the tree is 41.95 m.
Example 3 : A vertical flagpole of height 20 m casts a shadow 40 m long on horizontal ground. Calculate the angle of elevation of the sun, to the nearest minute.
tan θ = =
= 26° 34′
So the angle of elevation of the sun is 26° 34′