Class 10 Maths Chapter 9 Revision Notes - Applications of Trigonometry

Class 10 Maths Chapter 9 – Revision Notes

Line of sight: the line from the observer’s eye to the object being viewed.
Angle of elevation: angle between the horizontal and the line of sight when the object is above the horizontal level.
Angle of depression: angle between the horizontal and the line of sight when the object is below the horizontal level.
Core formula: height = distance × tanθ; distance = height / tanθ; line-of-sight length = height / sinθ = distance / cosθ.
Standard values: tan30° = 1/√3, tan45° = 1, tan60° = √3; sin30° = 1/2, sin45° = 1/√2, sin60° = √3/2.
Complementary-angle result: if elevations from distances p and q are complementary, height = √(pq).
Two-position (moving observer) formula: if elevation changes from θ to φ after moving distance a towards the object, height = a·tanθ·tanφ / (tanφ-tanθ).
Exam tip: always draw the right triangle and label the known angle/side before choosing a ratio.
Syllabus note (2026-27): only Exercise 9.1 (16 questions) is in the current rationalised syllabus; the old Exercise 9.2 was removed.