CBSE Class 10 Mathematics Chapter 9 Some Applications of Trigonometry — 20 MCQs with Answers

The angle of elevation is the angle between the horizontal line from the observer's eye and the line of sight to an object above. The angle of depression is the angle between the horizontal and the line of sight to an object below. Both angles are always measured from the horizontal — never from the vertical or the ground. NCERT Section 9.1 introduces these definitions with diagrams of a man looking at the top of a tower (elevation) or a boat from a cliff (depression). Confusion arises when students measure from the vertical; always draw the horizontal reference line first. Many board MCQs present a scenario and ask which angle — elevation or depression — is being described.

Most NCERT exercises and board papers start with problems where a single angle of elevation or depression and one side of a right triangle are given; students solve for the unknown side. The key is choosing the correct trigonometric ratio: tan θ when perpendicular and base are involved (most common), sin θ when hypotenuse and perpendicular are involved, cos θ when hypotenuse and base are involved. NCERT Example 9.1 shows a ladder leaning against a wall — given length (hypotenuse) and angle, find height reached. These one-step problems account for 60–70 per cent of CBSE MCQs in this chapter.

NCERT Exercise 9.1 Question 12 onwards introduces scenarios where the observer moves, creating two angles from two different points. For example, from a point the angle of elevation is 30°; after walking 20 m closer, it becomes 60°. Two equations are formed: tan 30° = h/x and tan 60° = h/(x – 20). Solving simultaneously gives both h and x. CBSE loves these as 3-mark subjectives, but occasionally MCQs test the setup or final value. Students must label distances carefully — draw a clear diagram showing both positions and the common height.

CBSE frequently embeds trigonometry in practical scenarios — estimating the height of an aeroplane, calculating the width of a river, measuring the distance a ship has sailed. These MCQs test whether students can extract the right triangle from the word problem. For instance, 'A man on a lighthouse 100 m high observes a boat at an angle of depression 30°; how far is the boat from the base?' translates to tan 30° = 100/d. NCERT includes river-width problems and aeroplane examples; recent board papers added drone surveillance and solar panel angles.

Since 2021, CBSE introduced assertion-reason MCQs: two statements are given, and students choose if both are true and Reason correctly explains Assertion, both true but Reason does not explain, Assertion true but Reason false, or both false. Chapter 9 assertions often pair a numerical result with a trigonometric fact. Case-based MCQs present a short paragraph (e.g. a surveyor measuring a hill) followed by 3–4 sub-questions. These are worth 1 mark each but require careful reading. NCERT does not have assertion-reason format, so students should practise from CBSE sample papers and previous years.

First, confusing angle of elevation with angle of depression costs marks; always draw the horizontal reference line. Second, using degrees when the calculator is in radian mode (or vice versa) yields bizarre answers. Third, forgetting to add the observer's height to the calculated height — many problems state 'a man 1.6 m tall stands 20 m away'; the tower height is h + 1.6, not h alone. Fourth, misidentifying the perpendicular and base in non-standard orientations (e.g. when the diagram shows a tilted view). Fifth, rounding intermediate steps too early; keep at least two decimal places or use exact surds until the final answer. CBSE mark schemes reward exact answers like 10√3 over 17.32.

Every MCQ in Chapter 9 hinges on substituting sin, cos or tan of 0°, 30°, 45°, 60° or 90°. NCERT Chapter 8 Table 8.1 lists these; students must memorise them cold. sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2. cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2. tan 30° = 1/√3, tan 45° = 1, tan 60° = √3. Forgetting that tan 90° is undefined causes wrong eliminations. Also remember cot θ = 1/tan θ, so cot 30° = √3, cot 45° = 1, cot 60° = 1/√3. Many MCQs give an answer in terms of √3; recognising 1/√3 ≈ 0.577 and √3 ≈ 1.732 helps cross-check reasonableness.

Some Applications of Trigonometry problems are visual — a poorly drawn triangle or mislabelled angle derails the entire solution. CBSETUTOR.ai offers a 24×7 AI tutor that accepts photo uploads of your NCERT exercise diagram or any coaching worksheet. Snap a picture of the problem, and the AI identifies the right triangle, labels sides, selects the correct trigonometric ratio, and walks you through the algebraic steps. It covers all 15 NCERT Exercise 9.1 questions plus additional CBSE sample paper MCQs. For ₹999 per month (one price for classes 6–12, all subjects), you get unlimited doubt solving — far cheaper than a single trigonometry tutor session in Delhi or Mumbai. Start with the 3-day free trial; solve five Chapter 9 problems with AI guidance, and watch your confidence soar. Parents love that usage reports show which subtopics the child practises most, making revision surgical rather than scattergun.

Chapter 9 typically contributes 2–3 marks in the CBSE Class 10 Maths paper — one 1-mark MCQ in Section A and sometimes a 2-mark or 3-mark subjective in Section B or C. For MCQs, spend no more than 45 seconds per question. First, draw a quick right triangle in the margin — this externalises your thinking and reduces errors. Second, identify the given angle and side, then pick tan if both legs are involved, sin/cos if hypotenuse appears. Third, substitute the exact trigonometric value (never approximate at this stage). Fourth, solve for the unknown algebraically; only then match with options. If two options are close (e.g. 10√3 vs 15√3), recompute or check units. Eliminate obviously wrong options first: if the tower is 10 m and you walk 5 m closer, the angle cannot decrease. Finally, if stuck beyond 60 seconds, mark your best guess and move on — trigonometry MCQs rarely carry bonus insight marks.