TRIGONOMETRY STUDY GUIDE — PART 2
Angles of Elevation & Depression and Word Problem Applications
1. ANGLES OF ELEVATION AND DEPRESSION
Real-world applications of trigonometry frequently involve measuring height and distance from a horizontal line
of sight.
Object (Upper)
Angle of Depression
Line of Sight
Angle of Elevation
bserver (Lower)
Key Concepts
Line of Sight: An imaginary straight line extending from the eye of an observer to the object being viewed.
Angle of Elevation: The angle formed between the horizontal line of sight and the line of sight up to an object
above the observer.
Angle of Depression: The angle formed between the horizontal line of sight and the line of sight down to an
object below the observer.
Note: The angle of elevation from point A to point B equals the angle of depression from point B to point A
(alternate interior angles).
Worked Example 1: Word Problem (Angle of Elevation)
A surveyor stands 50 meters away from the base of a building. Looking up to the top of the tower, the angle
of elevation is measured as 42°. Calculate the height of the building.
• Formulate equation: tan(42°) = Height / Distance = h / 50
• Solve: h = 50 × tan(42°) ≈ 50 × 0.9004 = 45.02 meters
Trigonometry Study Guide Pack — Part 2 Page 1 of 2
Angles of Elevation & Depression and Word Problem Applications
1. ANGLES OF ELEVATION AND DEPRESSION
Real-world applications of trigonometry frequently involve measuring height and distance from a horizontal line
of sight.
Object (Upper)
Angle of Depression
Line of Sight
Angle of Elevation
bserver (Lower)
Key Concepts
Line of Sight: An imaginary straight line extending from the eye of an observer to the object being viewed.
Angle of Elevation: The angle formed between the horizontal line of sight and the line of sight up to an object
above the observer.
Angle of Depression: The angle formed between the horizontal line of sight and the line of sight down to an
object below the observer.
Note: The angle of elevation from point A to point B equals the angle of depression from point B to point A
(alternate interior angles).
Worked Example 1: Word Problem (Angle of Elevation)
A surveyor stands 50 meters away from the base of a building. Looking up to the top of the tower, the angle
of elevation is measured as 42°. Calculate the height of the building.
• Formulate equation: tan(42°) = Height / Distance = h / 50
• Solve: h = 50 × tan(42°) ≈ 50 × 0.9004 = 45.02 meters
Trigonometry Study Guide Pack — Part 2 Page 1 of 2
