8
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
Angle of Elevation
Angle of Depression
Line of Sight
Horizontal Level
Heights of Towers & Buildings
Distance of Ships from Shore
Width of Rivers
Two Observers Problems
Problems with Two Angles of Elevation
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Basic | \(tan θ = Height / Horizontal Distance\) |
| sin θ | \(= Height / Slant Distance\) |
| cos θ | \(= Horizontal / Slant Distance\) |
| Two Angles | \(Use h = d·tan α = (d+x)·tan β and solve for unknowns\) |
Important Points to Remember
The angle of elevation is measured upward from the horizontal to the line of sight.
The angle of depression is measured downward from the horizontal to the line of sight.
For a tower of height h at a horizontal distance d: tan θ = h/d.
When the observer moves toward/away from the tower, use two equations and solve simultaneously.