CBSE Class 10 Mathematics Heights And Distances VBQs

Welcome! Check out the CBSE Class 10 Mathematics Heights And Distances VBQs right here. Built for the 2026-27 term, these Value Based Questions (VBQs) help Class 10 Mathematics students build strong moral values and practical life skills. Experienced teachers designed these materials to match current rules from CBSE, NCERT, and KVS.

Value Based Questions: Class 10 Mathematics Chapter 9 Some Applications of Trigonometry

Want to connect school lessons with real life? Solving Value Based Questions for Chapter 9 Some Applications of Trigonometry helps Class 10 students understand practical applications. These competency-based questions come with clear answers to help you get high marks in Class 10 and build good character.

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

Free study material for Mathematics

Ethics & VBQs Study Guide for Class 10 Mathematics

Download VBQs & Answers: Chapter 9 Some Applications of Trigonometry (Class 10 Mathematics)

Explore important Value-Based Questions (VBQs) for Chapter 9 Some Applications of Trigonometry structured according to the latest CBSE guidelines. These exercises help Class 10 learners grasp essential moral insights. Reviewing these solved answers builds analytical thinking and raises scores in Mathematics tests.

Important Solved Value-Based Questions for Chapter 9 Some Applications of Trigonometry

Crafted around the standard NCERT book for Class 10 Mathematics, these important questions aid thorough revision. Following your chapter practice, check our expert NCERT solutions for Class 10 Mathematics for deeper understanding.

Enhance Analytical Skills for Chapter 9 Some Applications of Trigonometry

Routine drills on these Class 10 Mathematics value problems enhance core understanding. Additional study materials for Chapter 9 Some Applications of Trigonometry are available on our site for extra support. Grasping these moral concepts lifts your test performance and highlights everyday uses of Mathematics.

FAQs

Where can I find 2026-27 CBSE Value Based Questions (VBQs) for Class 10 Mathematics Chapter 9 Some Applications of Trigonometry?

The latest collection of Value Based Questions for Class 10 Mathematics 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 9 Some Applications of Trigonometry VBQs?

Yes, all our Mathematics VBQs for 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 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 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 9 Some Applications of Trigonometry VBQs in PDF for free?

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