CBSE Class 10 Mathematics Heights And Distances VBQs

Read and download the CBSE Class 10 Mathematics Heights And Distances VBQs. Designed for the 2025-26 academic year, these Value Based Questions (VBQs) are important for Class 10 Mathematics students to understand moral reasoning and life skills. Our expert teachers have created these chapter-wise resources to align with the latest CBSE, NCERT, and KVS examination patterns.

VBQ for Class 10 Mathematics Chapter 9 Some Applications of Trigonometry

For Class 10 students, Value Based Questions for Chapter 9 Some Applications of Trigonometry help to apply textbook concepts to real-world application. These competency-based questions with detailed answers help in scoring high marks in Class 10 while building a strong ethical foundation.

Chapter 9 Some Applications of Trigonometry Class 10 Mathematics VBQ Questions with Answers

Value Based Questions

X-Mathematics

Topic-Heights and distances

1) A boy sees an injured cat on a window sill 20m above the ground. To help the cat the boy takes the staircase at an angle of elevation of 450

Contextual question: 

What is the distance the boy has to cover to reach the cat?

Value based question: 

What are the qualities the boy projects to help the cat?

KEY POINTS:

i) Compassion to animals

ii) Sympathy towards animals

iii) Responsibility

2) A paraglider when gliding 1000m above a forest notices a forest fire. He also observes two fire stations at angles of 450 and 600 on either side of the fire.

Contextual question: 

Find the distance of each fire station from the point of fire.

Value based question: 

Which station should the paraglider intimate first about the forest fire and what value do you learn from him?

KEY POINTS:

i) Social responsibility

ii) Presence of mind

iii) Quick decision

3) A builder is asked to build a decorative pillar 100m high. After the completion of the construction a surveyor came and viewed the top of the pillar from a point 55m away from the foot of the pillar at an angle of elevation of 300

Contextual question: 

What is the actual height of the pillar? (Take √3=1.732)

Value based question: 

Do you think that the builder must be paid fully? Justify your answer.

KEY POINTS

i) No, he has been dishonest.

ii) The builder has no moral values.

iii) He is against business ethics.

4) An air traffic controller instructs a plane on the edge of a runway to take of at 450. At the same time he instructs a plane flying at a height of 1km to descend at 300 to reach the edge so that both do not collide.

Contextual question: 

Find the difference in the heights of the planes at the instant when one plane is vertically above the other.

Value based question: 

What are the values you learn from the air traffic controller?

KEY POINTS:

i) Caring for the safety of the passengers.

ii) Precise planning and organizing.

iii) Commitments towards duty. 

5) A lighthouse 100m high emits light such that the farthest reach o f the light to the ship on the sea was an angle of 450◦.But it was noticed that many ships ran ashore and were wrecked.
 
Contextual question:
 
What should be the height of the lighthouse so that the reach of the light would be at an angle of 30◦.
 
Value based question:
 
What values do you think the authorities must posses to rectify the problem?
 
KEY POINTS:
 
i) Alert and responsible authorities.
 
ii) Trained personnel in disaster management.
 
iii) Immediate implementation of the solution to the problem.
 
6) The captain of ship A sees a distress flare fired by a ship in distress at an angle of elevation of 600. At the same instant the captain of ship B also sees the same flare at angle of elevation of 450. The flare is approximately 1000m above sea level.
 
Contextual question: Find the distance of both the ships from the ship in distress.
 
Value based question:  What qualities must the captains of both the ships possess to help the ship in distress?
 
KEY POINTS:
 
i) Presence of mind.
 
ii) Precise calculation.
 
iii) Humanity
 
iv)Team work.
 
7) Ram is standing on the window of the first floor of a building observes a per throwing a garbage into the dustbin which is 10m from the foot of the building with angle of depression of 450. He climbs to the window of second floor directly above the first floor and observes the same activity of the person with the angle of depression of the dustbin to be 600.
 
Contextual question 
 
Find the height of the first and second floor.
 
Value based Question: 
 
i.What values Should a person inculcate to keep the environment clean.
 
Key Points:
 
• Social responsibility
 
• Thoughtfulness
 
8) A flag staff stands on the top of 5m high tower .From a point on the ground the angle of elevation of the top of the flag staff is 600 and from the same point the angle of elevation of the top of the tower is 450.
 
Contextual question:
 
Find the height of the flag staff.
 
Value based Question: 
 
Mention any two ways in which every citizen of India should respect the national flag.
 
Key Points:
 
• Equality
 
• Harmony
 
• Unity
 
• Patriotism
 
 
Very Short Answer type Questions

Question. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Answer : 8 √3 m

Question. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
Answer : 16 (2/3)m

Question. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Answer : 3m, 2 √3 3m

Question. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Answer : 7( √3 + 1)m

Question. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Answer : 10 √3 m

Question. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Answer : 20( √3 − 1)m

Question. A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Answer : 0.8( √3 + 1)m

Question. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
Answer : 20 3m, 20m, 60m

Question. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Answer : 40 √3 m

Question. As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Answer : 75( √3 −1)m

Question. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Answer : 3 seconds

Question. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Answer : 19 √3 m

Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Mathematics VBQs Heights And Distances
CBSE Class 10 Mathematics VBQs Applications Of Trigonometry
CBSE Class 10 Mathematics Heights And Distances VBQs

Free study material for Chapter 9 Some Applications of Trigonometry

VBQs for Chapter 9 Some Applications of Trigonometry Class 10 Mathematics

Students can now access the Value-Based Questions (VBQs) for Chapter 9 Some Applications of Trigonometry as per the latest CBSE syllabus. These questions have been designed to help Class 10 students understand the moral and practical lessons of the chapter. You should practicing these solved answers to improve improve your analytical skills and get more marks in your Mathematics school exams.

Expert-Approved Chapter 9 Some Applications of Trigonometry Value-Based Questions & Answers

Our teachers have followed the NCERT book for Class 10 Mathematics to create these important solved questions. After solving the exercises given above, you should also refer to our NCERT solutions for Class 10 Mathematics and read the answers prepared by our teachers.

Improve your Mathematics Scores

Daily practice of these Class 10 Mathematics value-based problems will make your concepts better and to help you further we have provided more study materials for Chapter 9 Some Applications of Trigonometry on studiestoday.com. By learning these ethical and value driven topics you will easily get better marks and also also understand the real-life application of Mathematics.

Where can I find 2025-26 CBSE Value Based Questions (VBQs) for Class 10 Mathematics Chapter Chapter 9 Some Applications of Trigonometry?

The latest collection of Value Based Questions for Class 10 Mathematics Chapter Chapter 9 Some Applications of Trigonometry is available for free on StudiesToday.com. These questions are as per 2026 academic session to help students develop analytical and ethical reasoning skills.

Are answers provided for Class 10 Mathematics Chapter Chapter 9 Some Applications of Trigonometry VBQs?

Yes, all our Mathematics VBQs for Chapter Chapter 9 Some Applications of Trigonometry come with detailed model answers which help students to integrate factual knowledge with value-based insights to get high marks.

What is the importance of solving VBQs for Class 10 Chapter Chapter 9 Some Applications of Trigonometry Mathematics?

VBQs are important as they test student's ability to relate Mathematics concepts to real-life situations. For Chapter Chapter 9 Some Applications of Trigonometry these questions are as per the latest competency-based education goals.

How many marks are usually allocated to VBQs in the CBSE Mathematics paper?

In the current CBSE pattern for Class 10 Mathematics, Chapter 9 Some Applications of Trigonometry Value Based or Case-Based questions typically carry 3 to 5 marks.

Can I download Mathematics Chapter Chapter 9 Some Applications of Trigonometry VBQs in PDF for free?

Yes, you can download Class 10 Mathematics Chapter Chapter 9 Some Applications of Trigonometry VBQs in a mobile-friendly PDF format for free.