TRIGONOMETRY – PART 3: APPLICATIONS OF
TRIGONOMETRY
Heights and Distances:
Trigonometry helps us find the heights of objects and distances between points using angles of
elevation and depression.
Angle of Elevation:
The angle formed by the line of sight with the horizontal when the observer looks up is called the
angle of elevation.
Angle of Depression:
The angle formed by the line of sight with the horizontal when the observer looks down is called the
angle of depression.
Example Problem:
A 30 m tall tower casts a shadow 10√3 m long. Find the angle of elevation of the sun. tan θ =
Opposite / Adjacent = 30 / (10√3) = √3 → θ = 60°.
Summary:
• Use tan θ = h / d to relate height and distance. • Use complementary angles for indirect problems.
• Always draw a diagram before solving. Trigonometry forms the basis for many real-world
applications like navigation, surveying, and construction.
TRIGONOMETRY
Heights and Distances:
Trigonometry helps us find the heights of objects and distances between points using angles of
elevation and depression.
Angle of Elevation:
The angle formed by the line of sight with the horizontal when the observer looks up is called the
angle of elevation.
Angle of Depression:
The angle formed by the line of sight with the horizontal when the observer looks down is called the
angle of depression.
Example Problem:
A 30 m tall tower casts a shadow 10√3 m long. Find the angle of elevation of the sun. tan θ =
Opposite / Adjacent = 30 / (10√3) = √3 → θ = 60°.
Summary:
• Use tan θ = h / d to relate height and distance. • Use complementary angles for indirect problems.
• Always draw a diagram before solving. Trigonometry forms the basis for many real-world
applications like navigation, surveying, and construction.
