α h d tan α = h/d h = d·tan α DRAW DIAGRAM FIRST depression
tan α
Chapter 9  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Some Applications of Trigonometry

Draw the Diagram First — Every Heights and Distances Problem Becomes Simple

📋 50 MCQs ⭐ 28 PYQs ⏱ 80 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
18Easy
22Medium
10Hard
28PYQs
80 secAvg Time/Q
7Topics
Easy 36% Medium 44% Hard 20%

Why Practise These MCQs?

CBSE Class XNTSEState Boards

Applications of Trigonometry MCQs are almost entirely word problems — the concept is narrow but requires strong diagram-drawing skills. CBSE Boards assign a 4–5 mark problem from this chapter every year; MCQ practice here sharpens equation-setup speed. NTSE includes multi-step height and distance problems. All problems reduce to one of five standard diagram types.

Topic-wise MCQ Breakdown

Angle of Elevation (Single Observer)12 Q
Angle of Depression (From Height)8 Q
Two Observers / Two Positions10 Q
Ladder and Wall Problems5 Q
Tower and Shadow Problems6 Q
Flagpole / Building Problems5 Q
Combined Elevation + Depression4 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\tan\theta = \text{height}/\text{horizontal distance}$
$\sin\theta = \text{opposite}/\text{hypotenuse}$
$\cos\theta = \text{adjacent}/\text{hypotenuse}$
$\text{Elevation angle} = \text{Depression angle (alternate interior)}$
$\tan 30°=1/\sqrt{3},\ \tan 45°=1,\ \tan 60°=\sqrt{3}$

MCQ Solving Strategy

Step 1 for EVERY MCQ: draw the diagram. A labelled diagram converts the problem into a right triangle equation in under 30 seconds. Step 2: identify the angle (elevation or depression) and which sides are given/required. Step 3: write tan, sin, or cos equation and solve. For two-observer problems, write two separate equations and solve the system. Never guess from the numbers — always set up the equation.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Single elevation angle, find height given distance and angle

② Medium

Depression angle, find distance given height and angle

③ Hard

Two observers, find tower height using two angles simultaneously

★ PYQ

CBSE — 4-mark word problem with diagram; NTSE — multi-step height problem

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Circles
🎯 Knowledge Check

Maths — SOME APPLICATIONS OF TRIGONOMETRY

50 Questions Class 10 MCQs
1
The angle formed between the horizontal line of sight and the upward line of sight is called:
2
If \(\tan 45^\circ = 1\), then the height of a tower is equal to the distance of the observer when the angle of elevation is:
3
The angle of depression from a cliff to a boat is formed between:
4
If the angle of elevation to the top of a pole is \(30^\circ\) and its height is \(10\text{ m}\), the horizontal distance is:
5
In height-and-distance problems, the triangle formed is always:
6
A kite is \(50\text{ m}\) high. Angle of elevation is \(60^\circ\). Distance from observer is:
7
\(\tan 30^\circ =\)
8
A tower casts a \(20\text{ m}\) shadow at \(45^\circ\). Height is:
9
Which device is used for measuring angles in surveying?
10
If angle of depression is \(30^\circ\), angle of elevation from the lower point is:
11
Man sees top of tower at \(60^\circ\). Moves \(10\text{ m}\) closer ? angle becomes \(90^\circ\). Height =
12
For height \(h\), distance \(d\), elevation angle \(\theta\):
13
Balloon height \(100\text{ m}\). Angle \(30^\circ\). Distance =
14
\(\tan 60^\circ =\)
15
Cliff height \(80\text{ m}\). Depression \(45^\circ\). Distance =
16
Building height \(20\text{ m}\). Angle \(60^\circ\). Distance =
17
Maximum height for same distance occurs at:
18
Line of sight triangle in trigonometry is always:
19
Elevation = depression because of:
20
If height = shadow, angle =
21
Height \(h = d\tan\theta\) uses ratio:
22
If \(\tan\theta = 1\), then \(\theta\) is:
23
Which is NOT part of Class 10 applications?
24
Tower \(30\text{ m}\). Angle \(30^\circ\). Distance =
25
Height \(40\text{ m}\). Depression \(45^\circ\). Distance =
26
\(\sin 30^\circ =\)
27
Moving farther from object ? angle:
28
Right angle arises from:
29
Pole seen at \(45^\circ\). Distance \(12\text{ m}\). Height =
30
Height \(10\sqrt{3}\). Angle \(60^\circ\). Distance =
31
Most used ratio in height/distance:
32
If angle increases, observer is:
33
Balloon observed at two angles involves:
34
Tower \(50\text{ m}\). Shadow \(50\sqrt{3}\). Angle =
35
Airplane elevation increases means airplane is:
36
If object is above observer, angle is:
37
Distance is maximum when angle:
38
Height \(= d\sqrt{3}\) indicates angle:
39
Shadow = 0 means angle =
40
If angle = \(0^\circ\), height appears:
41
Two elevation angles ? form:
42
To compute height, we need:
43
Line of sight is drawn from:
44
\(\cos 60^\circ =\)
45
Angle of depression is measured from:
46
If tower height doubles, angle:
47
Looking down from balcony is:
48
\(\sin 60^\circ =\)
49
Maximum angle of elevation possible:
50
A tree has height \(h\). Angle = \(45^\circ\). Distance =
📚
ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
Sharing this chapter
Class 10 Maths Ch 9 MCQs: Applications of Trigonometry (Test)
Class 10 Maths Ch 9 MCQs: Applications of Trigonometry (Test) — Complete Notes & Solutions · academia-aeternum.com
This MCQ set has been meticulously designed to strengthen conceptual understanding and examination readiness for NCERT Class X Mathematics Chapter 9, Some Applications of Trigonometry. By covering definitions, principles, diagrams, angle relationships, and real-life height-and-distance scenarios, these questions help learners internalize the logic behind trigonometric applications rather than memorizing formulas mechanically. Each question is paired with a clear explanation to reinforce…
🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
Share on
WhatsApp
Telegram
X / Twitter
Facebook
Instagram
Threads
Pinterest
LinkedIn
Quora
Discord
Reddit
Email
academia-aeternum.com/class-10/mathematics/some-applications-of-trigonometry/mcqs/ Copy link
💡
Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

To apply trigonometric ratios (sin, cos, tan) to real-life problems involving heights and distances using angles of elevation and depression.

The straight, imaginary line joining the observer’s eye to the object being viewed.

The angle formed between the horizontal line of sight and the upward line of sight when an observer looks at an object above eye level.

The angle formed between the horizontal line of sight and the downward line of sight when an observer views an object below eye level.

Because the horizontal distance and vertical height naturally form perpendicular lines, creating right triangles useful for applying trigonometric ratios.

Primarily tangent (tan ?), but sine (sin ?) and cosine (cos ?) are also used depending on known sides.

tan ? = Opposite side / Adjacent side.

When the vertical height corresponds to the opposite side and the given length is the hypotenuse.

When the horizontal distance corresponds to the adjacent side and the given length is the hypotenuse.

Only standard angles (30°, 45°, 60°) are used, whose trigonometric ratios are known.

sin 30°=½, sin 45°=v2/2, sin 60°=v3/2; cos 30°=v3/2, cos 45°=v2/2, cos 60°=½; tan 30°=1/v3, tan 45°=1, tan 60°=v3.

Draw a clear, labeled diagram converting the scenario into a right triangle.

It helps identify the unknown side, the angle given, and the correct trigonometric ratio to use.

The imaginary line parallel to the ground passing through the observer’s eye.

The person, point, or object from which sight or measurement is taken.

Recent Posts

    --:-- ⏱ Time
    ⚡ Progress 0 / 50 answered

    SOME APPLICATIONS OF TRIGONOMETRY – Learning Resources

    Detailed Notes
    True / False
    NCERT Solutions
    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Class 10 Maths Ch 9 MCQs: Applications of Trigonometry (Test)
    Class 10 Maths Ch 9 MCQs: Applications of Trigonometry (Test) — Complete Notes & Solutions · academia-aeternum.com
    This MCQ set has been meticulously designed to strengthen conceptual understanding and examination readiness for NCERT Class X Mathematics Chapter 9, Some Applications of Trigonometry. By covering definitions, principles, diagrams, angle relationships, and real-life height-and-distance scenarios, these questions help learners internalize the logic behind trigonometric applications rather than memorizing formulas mechanically. Each question is paired with a clear explanation to reinforce…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-10/mathematics/some-applications-of-trigonometry/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.