📖 Chapter 9 — Some Applications of Trigonometry (CBSE Class 10 Maths): Detailed notes — heights & distances using angle of elevation and depression.
Chapter 9 — Some Applications of Trigonometry
👁️ 1. Line of Sight & Angles
- Line of sight: the line drawn from the observer's eye to the object.
- Angle of elevation: the angle between the line of sight and the horizontal, when the object is above (we look up).
- Angle of depression: the angle between the line of sight and the horizontal, when the object is below (we look down).
The angle of elevation of a point A from B equals the angle of depression of B from A (alternate angles).
📐 2. Method
Draw a right triangle; mark the height (opposite), base/distance (adjacent) and the given angle. Then use the correct ratio:
tan θ = height / base · sin θ = height / hypotenuse · cos θ = base / hypotenuse
Only the standard angles 30°, 45°, 60° are used. (At most two right triangles are involved.)
🧠 Remember: Elevation = look up, Depression = look down. Draw the triangle first. Use tan when height & base are involved, sin/cos when the hypotenuse (rope/slide) is involved. tan30°=1/√3, tan45°=1, tan60°=√3.
⭐ Exam Tips: ① Always draw a neat figure with the angle marked. ② Pick the ratio that connects the known and unknown sides. ③ Rationalise surds in the final answer. ④ For two observers/objects, form two equations and solve.