Heights and Distance Questions for IPMAT Exam 2027

Overview: Struggling with tricky triangles and tower angles? This blog covers the most important Heights and Distance Questions for IPMAT 2027 with answers to boost your accuracy and confidence.

Most of you might face difficulties when solving problems related to heights and distances, a subtopic of trigonometry.

However, if you follow the right methods to solve these questions, you can get them correct. 

This post shall take you through important questions based on heights and distances for IPMAT exams.

So, what are you looking for? Review the post to learn the expected Heights and Distance questions for IPMAT 2027 from trigonometry in the quant section.

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What are Heights and Distance Questions for IPMAT 2027 Preparation

Heights and distance are the main applications of trigonometry.

You will have to find the distance between two places, the height of an object, or the angle subtended by any object at a given point, without actually measuring the distance, height, or angles. 

To help you get an idea about the type of questions asked from this topic, we have provided important heights and distance questions that are curated from the previous year's IPMAT Question Papers.

Q) A vertical pole 15 m high casts a shadow 15 m long. Find the angle of elevation of the sun.

a) 30° 

b) 45° 

c) 60° 

d) 90°

Answer: (b) 45°

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Q) From the top of a building 80 m high, the angle of depression of a point on the ground is 30°. Find the distance of the point from the building.

a) 80√3 m 

b) 40 m 

c) 160 m 

d) 100 m

Answer: (a) 80√3 m

Q) A man standing 40 m away from a building observes the top of the building at 60° elevation. Find the height of the building.

a) 40 m 

b) 69.28 m 

c) 60 m 

d) 34.64 m

Answer: (b) 69.28 m

Q) The top of a hill is observed from two points at distances of 100 m and 150 m from the base. The angles of elevation are 45° and 30°, respectively. Find the height of the hill.

a) 100 m 

b) 75 m 

c) 86.6 m 

d) 90 m

Answer: (b) 75 m

Q) A boy flying a kite finds that the string makes an angle of 60° with the ground and is 100 m long. Find the height of the kite.

a) 50 m 

b) 86.6 m 

c) 60 m 

d) 100 m

Answer: (b) 86.6 m

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Q) The angle of elevation of the top of a tower from a point 60 m away is 30°. Find the height of the tower.

a) 20.5 m 

b) 34.6 m 

c) 60 m 

d) 103.9 m

Answer: (b) 34.6 m

Q) From the top of a 45 m building, the angle of depression of a car on the ground is 60°. Find the distance between the building and the car.

a) 30 m 

b) 45 m 

c) 77.9 m 

d) 25.9 m

Answer: (c) 77.9 m

Q) A tower is 100 m high. From a point on the ground, the angle of elevation of its top is 45°. Find the distance of the point from the base.

a) 50 m 

b) 70.7 m 

c) 100 m 

d) 141.4 m

Answer: (c) 100 m

Q) A boy is flying a kite with 120 m of string out, making a 30° angle with the ground. Find the height of the kite.

a) 60 m 

b) 80 m 

c) 100 m 

d) 120 m

Answer: (a) 60 m

Q) A 20 m tall tower casts a shadow of 11.55 m. Find the angle of elevation of the sun.

a) 30° 

b) 45° 

c) 60° 

d) 70°

Answer: (c) 60°

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Sample Heights and Distance Questions for IPMAT Exam with Answers

The questions based on heights and distance are quite lengthy and time-consuming. Therefore, following the IPMAT Preparation Tips provided by experts will help you solve these questions in seconds.

Q) A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a lighthouse as 60⁰ and the angle of depression of the base of the lighthouse as 30⁰. Find the height of the lighthouse.

a) 30m

b) 40m

c) 45m

d) 38m

Answer: (b) 40m

Q) From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β, respectively. Find the height of the second building.

a) 60(1+ tan α tanβ)

b) 60(1+ cot α tanβ)

c) 60(1+ tan α cotβ)

d) 60(1- tan αcotβ)

Answer: (c) 60(1 + tan α cotβ)

Q) From the top of a tower 75m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 300 and 450, respectively. Find the height of the pole.

a) 30.4m

b) 35.9m

c) 28.6m

d) 31.7m

Answer: (d) 31.7m

Q) The angle of elevation of the top of a tower from point A on the ground is 30⁰. On moving a distance of 40m towards the foot of the tower, the angle of elevation increases to 45⁰. Find the height of the tower.

a) 48.6m

b) 42.84m

c) 54.64m

d) 58.76m

Answer: (a) 48.6m

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Q) A man observes the angle of elevation of the top of a tower as 30°. If the tower is 100 m high, find the distance of the man from the tower.

a) 173.2 m 

b) 86.6 m 

c) 100 m 

d) 150 m

Answer: (a) 173.2 m

Q) From a point on the ground, the angle of elevation of a pole is 60°. If the height of the pole is 20√3 m, find the distance from the point to the base.

a) 20 m 

b) 30 m 

c) 40 m 

d) 60 m

Answer: (b) 20

Q) A tower casts a shadow of 20 m when the angle of elevation of the sun is 45°. Find the height of the tower.

a) 10 m 

b) 20 m 

c) 30 m 

d) 40 m

Answer: (a) 20 m

Q) A ladder 10 m long leans against a wall making a 60° angle with the ground. Find the height it reaches on the wall.

a) 5 m 

b) 10 m 

c) 8.66 m 

d) 6.5 m

Answer: (c) 8.66 m

Additional Heights and Distance Questions for IPMAT 2027 Exam with Answers

Q) From the top of a 50 m high tower, the angle of depression to a car is 30°. Find the distance of the car from the base of the tower.

a) 50√3 m 

b) 25 m 

c) 86.6 m 

d) 100 m

Answer: (c) 86.6 m

Q) The angle of elevation of the top of a tower from a point 100 m away is 45°. Find the height of the tower.

a) 100 m 

b) 50 m 

c) 70.7 m 

d) 80 m

Answer: (a) 100 m

Q) A tree broken by the wind falls so that its top touches the ground 12 m from the base. If the broken part makes a 60° angle with the ground, find the height of the tree.

a) 24 m 

b) 18 m 

c) 30 m 

d) 26 m

Answer: (a) 24 m

Q) From the top of a lighthouse 60 m high, the angle of depression to a boat is 60°. Find the distance of the boat from the base of the lighthouse.

a) 30 m 

b) 45 m 

c) 60√3 m 

d) 90 m

Answer: (c) 60√3 m

Q) A man sees the top of a tower at an angle of elevation of 30°. After walking 50 m closer, the angle becomes 60°. Find the height of the tower.

a) 43.3 m 

b) 50 m 

c) 25 m 

d) 30 m

Answer: (a) 43.3 m

Q) The angle of elevation of a balloon from a point on the ground is 45°. If the balloon is 100 m high, find its horizontal distance from the point.

a) 100 m 

b) 70.7 m 

c) 141.4 m 

d) 50 m

Answer: (a) 100 m

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How to Prepare for Heights and Distance Questions for IPMAT 2027?

#1 Master Basic Trigonometric Ratios

Familiarize yourself with standard trigonometric values for angles like 30°, 45°, and 60°, as most IPMAT questions are based on these. Knowing sin, cos, and tan values by heart will save time during the exam.

#2 Visualise the Problem with Diagrams

Convert word problems into right-angled triangle diagrams. This will help you understand the relationship between the observer, the object, and the angles involved, making it easier to apply the correct formula.

#3 Revise Key Formulas Regularly

Keep a formula sheet for quick revision of essential trigonometric identities and height-distance relationships. Practice applying these formulas through short exercises and daily quizzes.

#4 Practice a Wide Range of Questions

Exposure to various question types involving angles of elevation and depression will enhance your problem-solving flexibility. Include both easy and moderate-level problems in your practice routine.

#5 Focus on Speed and Accuracy with Timed Practice

Solve questions with a timer to build your speed. Analyse your mistakes and time taken for each question to gradually improve accuracy and performance under pressure.

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Key Takeaways

• Master basic trigonometric ratios like sin, cos, and tan for common angles (30°, 45°, 60°).
• Visualise the problem using right-angled triangle diagrams to understand the given scenario.
• Revise the height-distance formulas and apply them to real-world examples to improve retention.
• Practice a variety of questions involving elevation and depression angles to build speed and accuracy.
• Focus on time management by solving timed mock questions regularly to simulate exam conditions.
• Practice IPMAT 2027 Distance and Practice Questions to strengthen your prep.