Heights and Distances

• Model real situations with right triangles (angle of elevation/depression).
• Choose correct ratio: sin, cos, or tan.
• Draw a clear diagram before calculating.

1. Angle of elevation — angle from horizontal up to object.
2. Angle of depression — angle from horizontal down (equal to elevation from other point).
3. Line of sight — from observer to object.
4. Strategy — label height h, distance d; use tan θ = h/d when opposite/adjacent known.
5. NCERT — tower problems, shadow problems, two-point observation.

A tower casts a shadow 10 m long when sun's elevation is 45°. Find height.

tan 45° = h / 10
1 = h / 10
h = 10 m

• Using angle of depression from vertical instead of horizontal.
• Confusing height of observer with height of object.
• Forgetting units (metres) in final answer.

• Define angle of elevation with a sketch.
• From 20 m away, top of pole subtends 60°. Find height (use tan 60° = √3).
• Why are depression and elevation equal for two horizontal lines?

Open the Practice tab for graded questions on Heights and Distances.