IPMAT Trigonometry Questions with Solutions [Solved Examples]

Overview: Are you ready to tackle IPMAT Trigonometry Questions 2026 like a pro? These questions are a staple in the Quantitative section and can really help you score high if approached correctly.

If you're preparing for the IPMAT 2026 exam, one topic you simply can't afford to skip is Trigonometry.

Every year, the IPMAT Trigonometry Questions section forms a crucial part of the Quantitative Aptitude paper.

Students often fear this topic because of the formulas, ratios, and geometry involved - but once you understand the logic behind it, it becomes one of the easiest and most scoring areas in the entire IPMAT syllabus.

In this detailed guide, we'll break down everything you need to know about IPMAT Trigonometry Questions 2026 - concepts, formulas, problem types, previous year trends, shortcuts, and smart strategies to solve them fast.

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IPMAT Trigonometry Questions 2026 - Step-by-Step Solved Examples

Q1. A kite is flying with a thread 150 meters long. If the thread makes an angle of 60° with the horizontal, find the height of the kite from the ground.

Options:

(a) 50 m

(b) 25√3 m

(c) 75√3 m

(d) 80 m

✅ Answer: (c) 75√3 m

Explanation: Height = 150 × sin(60°) = 150 × (√3/2) = 75√3 m

Q2. A vertical post 15 ft high is broken at a certain height, and its upper part touches the ground making an angle of 30° with it. Find the height at which the post is broken.

Options:

(a) 5 ft

(b) 10 ft

(c) 5√3 ft

(d) 10√3 ft

✅ Answer: (a) 5 ft

Explanation: Total length = 3x = 15 → x = 5 ft → broken at 5 ft height.

Q3. A man observes the top of a tower at an elevation of 30°. After walking some distance towards the tower, the angle becomes 60°. If the tower's height is 30 m, find the distance he moved.

Options:

(a) 22 m

(b) 20 m

(c) 22√3 m

(d) 20√3 m

✅ Answer: (d) 20√3 m

Explanation: Using tan(θ), distance moved = 20√3 m

Q4. The angle of elevation of an airplane from a point on the ground is 60°. After 15 seconds, it becomes 30°. If the airplane is flying at a height of 1500√3 m, find its speed.

Options:

(a) 300 m/s

(b) 100 m/s

(c) 200 m/s

(d) 150 m/s

✅ Answer: (c) 200 m/s

Explanation: Distance covered = 3000 m in 15 sec → Speed = 200 m/s

Q5. Two vertical pillars of heights 16 m and 9 m stand on level ground at a distance of x m apart. If the angles of elevation of their tops from the bottoms of the other are complementary, find x.

Options:

(a) 15 m

(b) 12 m

(c) 16 m

(d) 9 m

✅ Answer: (b) 12 m

Explanation: tan θ × cot θ = 1 → (16/x)(9/x) = 1 → x² = 144 → x = 12 m

Q6. Two vertical posts stand on opposite sides of a road. One post is 108 m high. From the top of this post, the angles of depression of the top and the foot of the other post are 30° and 60°, respectively. Find the height of the other post.

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Options:

(a) 36 m

(b) 108 m

(c) 72 m

(d) 110 m

✅ Answer: (c) 72 m

Explanation: Height difference = 108 - 36 = 72 m

Q7. The angle of elevation of the top of a tower from a point 60 m away from its foot is 45°. Find the height of the tower.

Options:

(a) 30 m

(b) 45 m

(c) 60 m

(d) 90 m

✅ Answer: (c) 60 m

Explanation: tan(45°) = h / 60 → h = 60 × 1 = 60 m

Q8. From the top of a lighthouse 100 m high, the angle of depression of a ship is 30°. Find the distance of the ship from the foot of the lighthouse.

Options:

(a) 100√3 m

(b) 150 m

(c) 200√3 m

(d) 300 m

✅ Answer: (a) 100√3 m

Explanation: tan(30°) = 100 / d → d = 100 / (1/√3) = 100√3 m

Q9. The shadow of a tower is √3 times the height of the tower. Find the angle of elevation of the sun.

Options:

(a) 30°

(b) 45°

(c) 60°

(d) 90°

✅ Answer: (a) 30°

Explanation: tan(θ) = height / shadow = 1 / √3 → θ = 30°

Q10. The angle of elevation of the top of a building from a point on the ground is 45°. After moving 20 m closer, the angle becomes 60°. Find the height of the building.

Options:

(a) 20 m

(b) 30√3 m

(c) 20√3 m

(d) 40 m

✅ Answer: (c) 20√3 m

Explanation: Using tan(45°) = h/x and tan(60°) = h/(x−20), solving gives h = 20√3 m

Q11. A man standing on a tower observes a car moving directly towards him. The angle of depression changes from 30° to 60° in 5 minutes. If the height of the tower is 150 m, find the speed of the car.

Options:

(a) 25√3 m/s

(b) 10 m/s

(c) 5√3 m/s

(d) 15 m/s

✅ Answer: (b) 10 m/s

Explanation: tan(30°) = 150 / x₁ → x₁ = 150√3 tan(60°) = 150 / x₂ → x₂ = 150 / √3 Distance covered = 150√3 − 150/√3 = 200√3 m Speed = (200√3) / (5 × 60) = 10 m/s

Q12. From the top of a 50 m tower, the angle of depression of a car on the ground is 60°. Find the distance of the car from the foot of the tower.

Options:

(a) 25 m

(b) 50√3 m

(c) 50/√3 m

(d) 100 m

✅ Answer: (c) 50/√3 m

Explanation: tan(60°) = 50 / x → x = 50 / √3 m

Q13. The top of a 20 m high building is observed at an elevation of 30° from a point A on the ground. Find how far A is from the building.

Options:

(a) 10√3 m

(b) 20√3 m

(c) 15√3 m

(d) 30√3 m

✅ Answer: (b) 20√3 m

Explanation: tan(30°) = 20 / x → x = 20√3 m

Q14. A man is watching a balloon moving vertically upwards. The angle of elevation changes from 30° to 60° as the balloon rises 60 m. Find the height of the balloon above the ground when the angle is 60°.

Options:

(a) 40 m

(b) 60 m

(c) 80 m

(d) 100 m

✅ Answer: (d) 100 m

Explanation: Let initial height be h. tan(60°) = (h + 60)/x and tan(30°) = h/x → Solving gives h = 40 → Total height = 100 m

Q15. From the top of a building 80 m high, the angle of elevation of the top of a tower is 30°, and the angle of depression of its foot is 45°. Find the height of the tower.

Options:

(a) 80 + 80/√3 m

(b) 80 + 80√3 m

(c) 40 + 40√3 m

(d) 60 m

✅ Answer: (a) 80 + 80/√3 m

Explanation: Let distance between tower and building be x. tan(45°) = 80/x → x = 80 tan(30°) = (H − 80)/80 → H = 80 + 80/√3 m

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Why Trigonometry Matters in IPMAT 2026

Many students feel nervous when they hear "trigonometry," imagining complicated formulas and confusing triangles.

But in the IPMAT Trigonometry Questions 2026, the reality is simple:

You only need to understand right-angled triangles and their side-angle relationships.

No calculus. No heavy identities. Just visualization, ratios, and logic.

Trigonometry = Geometry + Ratios + Common Sense.

Once you understand the logic, every question becomes a 60-second problem.

Understanding the Importance of IPMAT Trigonometry Questions 2026

Trigonometry questions in IPMAT appear almost every year, both in IIM Indore and IIM Rohtak question papers.

These questions generally test your understanding of angles, trigonometric ratios, identities, and real-life applications such as height and distance.

On average, you can expect 2-4 IPMAT Trigonometry Questions, each carrying equal marks.

The best part? Most of them are formula-based, meaning that if you know your basics well, these are guaranteed marks.

Common Types of IPMAT Trigonometry Questions 2026

Understanding question patterns helps you recognize what the examiner expects.

Let's go through the most repeated types of IPMAT Trigonometry Questions with examples.

1. Height and Distance (Angle of Elevation / Depression)

Most Frequent Topic (5-6 marks potential)

Concept: These questions involve using trigonometric ratios (sin, cos, tan) in right-angled triangles formed by vertical and horizontal lines.

Example:

A tower is 50 m high. The angle of elevation of its top from a point on the ground is 30°. Find the distance of the point from the tower's base.

Formula:

tan⁡θ=heightbase\tan \theta = \frac{\text{height}}{\text{base}}tanθ=baseheight​

Tip: Always draw a diagram and use standard triangle ratios:

• 30°-60°-90° → 1 : √3 : 2

• 45°-45°-90° → 1 : 1 : √2

2. Angle of Elevation Change Problems

Concept: A person moves towards or away from an object, changing the angle of elevation.

Example:

A man sees a tower at 30°. After walking 40 m towards it, the angle becomes 60°. Find the height of the tower.

Tip: Use two tan equations and eliminate distance to find height.

3. Complementary Angle Questions

Concept: When one angle is the complement of another (θ + φ = 90°), then:

sin⁡θ=cos⁡ϕ,tan⁡θ=cot⁡ϕ\sin \theta = \cos \phi, \quad \tan \theta = \cot \phisinθ=cosϕ,tanθ=cotϕ

Example:

Two poles have heights 16 m and 9 m, and angles of elevation from each other's bases are complementary. Find the distance between them.

Tip: Set up:

tan⁡θ=16x,cot⁡θ=9x\tan \theta = \frac{16}{x}, \quad \cot \theta = \frac{9}{x}tanθ=x16​,cotθ=x9​

Multiply and solve → x2=144x^2 = 144x2=144, so x=12x = 12x=12.

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4. Moving Object Problems (Airplane, Balloon, or Boat)

Concept: The angle of elevation/depression of a moving object changes over time.

Example:

An airplane at 1500√3 m height changes its angle of elevation from 60° to 30° in 15 seconds. Find its speed.

Tip: Use tan θ = height / distance → Find horizontal distances for both angles, subtract to get distance covered, divide by time for speed.

5. Trigonometric Ratio Value Questions

Concept: Direct evaluation of trigonometric ratios without a figure.

Example:

If sin θ = 3/5, find cos θ and tan θ.

Solution: Use Pythagoras → cos θ = 4/5, tan θ = 3/4.

Tip: Remember the trigonometric identities:

sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1

6. Angle Relationships & Identities

Concept: Simplify or prove expressions using basic trigonometric formulas.

Example:

Simplify: 1−sin⁡2Acos⁡2A\frac{1 - \sin^2 A}{\cos^2 A}cos2A1−sin2A​

Solution: Since 1−sin⁡2A=cos⁡2A1 - \sin^2 A = \cos^2 A1−sin2A=cos2A, the result = 1.

Tip: These are direct formula-based questions - memorize key identities for quick wins.

Answer: 45\frac{4}{5}54​

Core Idea Behind IPMAT Trigonometry Questions 2026

All questions are based on right-angled triangles formed between:

1. The line of sight,
2. The horizontal ground, and
3. The vertical object (building, tower, pole, etc.).

Trigonometric ratios define the relationship between sides and angles.

The Six Trigonometric Ratios

Ratio	Formula	Meaning
sin θ	P / H	Perpendicular ÷ Hypotenuse
cos θ	B / H	Base ÷ Hypotenuse
tan θ	P / B	Perpendicular ÷ Base
cot θ	B / P	Base ÷ Perpendicular
sec θ	H / B	Hypotenuse ÷ Base
cosec θ	H / P	Hypotenuse ÷ Perpendicular

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Core Application - Height and Distance (Main Focus for IPMAT Trigonometry Questions 2026)

If you want to score high in IPMAT 2026, mastering Height and Distance problems is essential.

These problems form the backbone of IPMAT Trigonometry Questions 2026 because they combine geometry, logic, and basic trigonometry in a way that is always straightforward if approached correctly.

What Are Height and Distance Problems?

At their core, these problems deal with right-angled triangles formed between:

1. The observer's line of sight,
2. The horizontal ground, and
3. The vertical object (like a tower, building, or kite string).

Two key angles appear in these problems:

• Angle of Elevation: This is the angle formed when the observer looks upwards from their eye level to the top of an object. For example, looking at a kite in the sky or at the top of a tall tower.

• Angle of Depression: This is the angle formed when the observer looks downwards from their eye-level to the bottom of an object. For instance, looking down from a balcony or the top of a building at a car on the road.

Why This Section Is Crucial?

• High Frequency: Almost every IPMAT paper contains at least one Height and Distance question. Sometimes it's a simple single-triangle problem, other times it involves multiple steps like moving observers, broken objects, or complementary angles.

• High Accuracy Potential: These questions are purely formulaic once you visualize the triangle correctly. Students who practice these can often solve them in under 2 minutes, making them some of the highest-scoring questions in Quantitative Aptitude.

• Foundational for Other Problems: Understanding these problems also helps with motion problems (like airplanes or cranes) and complementary angles between pillars or towers.

How to Approach IPMAT Trigonometry Questions 2026 in Height and Distance?

1. Draw the triangle first. Never attempt to solve without a diagram. Visualizing the perpendicular (height), base (distance), and hypotenuse is critical.
2. Identify what is known and unknown. Are you given the height or the hypotenuse? Are you asked to find the distance or the height?
3. Select the correct trigonometric ratio.

• Use sinθ = opposite/hypotenuse if the hypotenuse is given.
• Use tanθ = opposite/adjacent if the horizontal distance is given.

1. Watch for 30°-60°-90° and 45°-45°-90° triangles. Many questions reduce to these special triangles, making calculations fast and easy.
2. Check angles of elevation and depression. Remember: Angle of depression = Angle of elevation from the other point.

Key Definitions

Term	Explanation
Angle of Elevation	The angle formed when the observer looks upward from the horizontal line.
Angle of Depression	The angle formed when the observer looks downward from the horizontal line.
Line of Sight	The imaginary line connecting the observer's eye and the object.

Special Triangles You MUST Remember for IPMAT Trigonometry Questions

1. The 30°-60°-90° Triangle

Ratio → 1 : √3: 2 If the side opposite 30° = x → Opposite 60° = x√3 → Hypotenuse = 2x

Remember: 30° → smallest side 60° → medium side 90° → longest side

2. The 45°-45°-90° Triangle

Ratio → 1: 1: √2 If one perpendicular = x → Other = x → Hypotenuse = x√2

Remember: Both perpendicular sides are equal in a 45° triangle.

Quick Trigonometric Values

θ	sin θ	cos θ	tan θ
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	∞

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Common Mistakes in IPMAT Trigonometry Questions

1. ❌ Mixing up base and perpendicular. (Tip: Base = ground distance, Perpendicular = height.)
2. ❌ Using sin instead of tan when the hypotenuse is not given.
3. ❌ Forgetting that angle of depression = angle of elevation.
4. ❌ Not converting time or distance units in motion problems.
5. ❌ Rushing without drawing the triangle.

Conceptual Advice For IPMAT Trigonometry Questions

"Every IPMAT height and distance question is just a variation of a single right triangle."

So instead of memorizing formulas, focus on visualizing the triangle:

• Which side is known?
• Which angle is given?
• Which side are we finding?

Once you can answer those, the formula reveals itself automatically.

"Draw before you solve. Always."

Visualization is your secret weapon.

In the IPMAT Trigonometry Questions 2026, most students lose marks not because they can't calculate - but because they can't see the triangle.

Once you can picture the right triangle, you'll find that every trigonometry question - from a kite to an airplane- is just a familiar friend.

The IPMAT Trigonometry Questions 2026 aren't meant to test how many formulas you remember; they test how well you can think geometrically.

IPMAT 2026 Trigonometry Weightage

Type	Expected No. of Questions	Difficulty	Marks
Height & Distance	1-2	Moderate	4-8
Ratio Simplification	1	Easy	4
Complementary Angles	1	Easy	4

Total: 3-4 questions, worth 12-16 marks - extremely high scoring if prepared well.

Practice Strategy for IPMAT Trigonometry Questions 2026

1. Learn through visualization.
2. Practice 20-25 height & distance questions.
3. Memorize special triangles (1√3:2 and 1:1√2).
4. Revise daily - trigonometry fades fast without repetition.
5. Time yourself - aim for under 2 minutes per question.

Quick Revision Table for IPMAT Trigonometry Questions 2026

Formula	Used When	Example
sinθ = P/H	Height with hypotenuse	Kite problem
tanθ = P/B	Height with base	Tower & man
tan(90°−θ)=cotθ	Complementary angles	Two pillars
Speed = Distance/Time	Motion	Airplane problem

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Key Takeaways 

1. Always Draw a Diagram: Visualizing the triangle makes IPMAT Trigonometry Questions 2026 much easier to solve.
2. Identify Right Triangles: Most Trigonometry Questions reduce to right-angled triangles. Identify the perpendicular (height), base (distance), and hypotenuse correctly.
3. Use Trigonometric Ratios Accurately: Apply tanθ = opposite/adjacent, sinθ = opposite/hypotenuse, or cosθ = adjacent/hypotenuse depending on what the question asks.
4. Leverage Special Triangles: Memorize 30°-60°-90° (x, √3x, 2x) and 45°-45°-90° (x, x, x√2) triangles to save time on calculations. These appear repeatedly in IPMAT Trigonometry Questions 2026.
5. Understand Complementary Angles: Many IPM Trigonometry Questions 2026 use complementary angles; cotθ and tanθ relationships help calculate distances quickly.
6. Break Moving Observer/Objects Problems Step-by-Step: Divide them into initial and final positions for clarity when solving Trigonometry Questions.
7. High Score Opportunity: Since Trigonometry Questions follow predictable formulas, consistent practice can help secure marks quickly.
8. Check Units and Precision: Always verify meters vs. feet and maintain accuracy to avoid errors in IPMAT Trigonometry Questions 2026.