Chapter 9 · Class X Mathematics · NCERT Exercises

Some Applications of Trigonometry — Exercises

Heights & Distances — All 16 Application Problems Fully Solved

📂 1 Exercise 📝 16 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 9.1

Angle of elevation; angle of depression; heights and distances

16 Q Moderate-Hard

1 exercise file · 16 total questions

Chapter at a Glance

CBSE BoardsNTSE

5 Concepts

4 Formulas

Moderate Difficulty

5–7% Weightage

Before You Begin

Prerequisites

✓Ch 8 — Trigonometry ratios and standard values
✓Pythagoras Theorem
✓Properties of parallel lines

Have Ready

🔧Rough diagram on graph paper
🔧tan/sin/cos standard values card

Exercise Topic Map

Exercise 9.1 Draw clear diagram; mark angle of elevation/depression; identify right triangle; apply tanθ = opp/adj for most problems; combine two triangles for "from both ends" problems

Key Formulae — Recall Before Solving

\(\tan\theta = \dfrac{\text{height}}{\text{horizontal distance}} \quad \text{(angle of elevation)}\)

\(\text{Angle of depression} = \text{Angle of elevation (alternate angles)}\)

\(\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}};\quad \cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}\)

\(\text{If two observers: form two equations; solve simultaneously}\)

NCERT Solving Method

Step 1 — ALWAYS draw a clear, labelled diagram first; this chapter is entirely diagram-based. Step 2 — Mark angles of elevation (looking up) and depression (looking down) correctly at the observer's position. Step 3 — Angle of depression = angle of elevation (alternate interior angles with horizontal). Step 4 — Two-observation problems: let unknown height = h, distance = x/d; form two tan equations; divide or subtract to eliminate one variable.