NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 Some Applications of Trigonometry in Hindi and English Medium updated for Session 2024-25. Class 10 Maths Exercise 9.1 Height and Distance is given here in simplified format with video solution.

Class 10 Maths Exercise 9.1 Solutions

Class 10 Maths Exercise 9.1 in Hindi Medium

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10th Maths Chapter 9 Solutions

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To study Class 10 Maths Exercise 9.1, start by reviewing the basic trigonometric ratios and their practical applications, particularly focusing on right-angled triangles. You will often encounter questions that ask you to calculate the height of an object or the distance from a point to an object based on the given angle of elevation or depression. Practice drawing diagrams to visually represent the problems, as this will help you understand the relationships between angles and distances. Make sure you can identify which trigonometric ratio (sine, cosine, or tangent) to use depending on the information provided in the question (e.g., opposite side, adjacent side, or hypotenuse).

When preparing for the exam, practice solving different types of problems where the angle of elevation or depression is given. Use the examples in the textbook, and solve them multiple times to become familiar with common patterns. Focus on problems that require multiple steps, such as finding both the height of an object and the distance from the observer to the object. Also, remember to pay attention to the units of measurement and ensure you can convert between them if necessary. Practice solving each exercise within a set time limit to build speed and accuracy, both of which are essential during exams.

## Class 10 Maths Exercise 9.1 Questions in Detail

- A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.
- 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.
- 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 is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have 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?
- 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.
- 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.
- 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.
- 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.
- 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.
- The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of 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.
- 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.
- A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
- 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.
- 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.
- A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
- 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.

Class: 10 | Maths Solutions |

Chapter 9: | Exercise 9.1 |

Topic Name: | Height and Distance |

Content Type: | Text, Videos, Images and PDF |

Session: | CBSE 2024-25 |

Medium: | English and Hindi Medium |

### NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 PDF

Class 10 Maths Exercise 9.1 in PDF format free download Hindi Medium and English Medium or View in Video Format updated for academic session 2024-25. All NCERT Solutions and Offline Apps 2024-25 are free use online for all CBSE and UP Board High School students who are using NCERT Books for their exams. Download Offline apps and PDF Solutions free for offline use.

### 10 Maths Chapter 9 Exercise 9.1 Solutions

NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 Some Applications of Trigonometry – Height and Distance questions in PDF form to free download and for online use also, updated for new academic session 2024-25. Visit to Class 10 Maths Chapter 9 main page for other exercises whether download or online study.

#### Questions for Practice with Answers

1. An aeroplane, when 3000 m high, passes vertically above another plane at an instant when the angle of elevation of two aeroplanes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the two planes. [Answer: 1268 m]

2. The angle of elevation of a cloud from a point 60 metres above a lake is 30° and the angle of depression of its reflection of the cloud in the lake is 60°. Find the height of the cloud. [Answer: 120 m]

3. A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45°. The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 30°. Find the speed of flying of the bird. [Answer: 29.28 m]

4. From the top of a 7 m high building, the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is 30°. Find the height of the tower. [Answer: 28 m]

##### Frequently Asked Questions with Answers

1. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl, standing on the roof of 20 m high building, finds the angle of elevation of the same bird to be 45°. Both the boy and girl are on the opposite sides of the bird. Find the distance of bird from the girl. [Answer: 30√2 m]

2. Anand is watching a circus artist climbing a 20m long rope which is tightly stretched and tied from the top of vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°. [Answer: 10 m]

3. From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be 30° and 45°. Find the height of the hill. [Answer: 1.37 km]

4. The string of a kite is 150 m long and it makes an angle 60° with the horizontal. Find the height of the kite above the ground. (Assume string to be tight). [Answer: 75√3]

5. The upper part of a tree broken over by the wind makes an angle of 30° with the ground and the distance of the root from the point where the top touches the ground is 25 m. What was the height of the tree? [Answer: 43.3 m]

###### Questions from the Board Papers

1. A vertical flagstaff stands on a horizontal plane. From a point 100 m from its foot, the angle of elevation of its top is found to be 45°. Find the height of the flagstaff. [Answer: 100 m] 15. The shadow of a vertical tower on level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. Find the height of the tower. [Answer: 13.65 m]

2. An aeroplane at an altitude of 200 m observes angles of depression of opposite points on the two banks of the river to be 45° and 60°, find the width of the river. [Answer: 315.8 m]

3. A fire in a building ‘B’ is reported on telephone in two fire stations P an Q, 20 km apart from each other on a straight road. P observes that the fire is at an, angle of 60° to the road, and Q observes, that it is at an angle of 45° to the road. Which station should send its team and how much distance will this team has to travel? [Answer: Station P, 14.64 km]

4. A 1.2 m tall girl spots a balloon on the eve of Independence Day, moving with the wind in a horizontal live at a height of 88.2 m from the ground. The angle of elevation of the balloon from the girl at an instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon. [Answer: 58√3 m]

###### Important Questions for Practice

1. As observed from the top of a light house, 100 m high above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 60°. Determine the distance travelled by the ship during the period of observation. [Answer: 115.5 m]

2. The angles of elevation and depression of the top and bottom of a light house from the top of a building 60 m high are 30° and 60° respectively. Find (i) The difference between the height of the light house and the building. (ii) distance between the light house and the building. [Answer: 20 m, 34.64 m]

3. The angles of elevation of the top of a tower from two points on the ground at distances 9 m and 4 m from the base of the tower are in the same straight line with it are complementary. Find the height of the tower. [Answer: 6 m]

4. A man standing on the deck of a ship, 10 m above the water level observes the angle of elevation of the top of a hill as 60° and angle of depression the bottom of a hill as 30°. Find the distance of the hill from the ship and height of the hill. [Answer: 40 m, 17.32 m]

###### Common Questions in all Exams

1. A 7 m long flagstaff is fixed on the top of a tower on the horizontal plane. From a point on the ground, the angle of elevation of the top and the bottom of the flagstaff are 45° and 30° respectively. Find the height of the tower. [Answer: 9.6 m]

2. The angle of elevation of a tower at a point is 45°. After going 40 m towards the foot of the tower, the angle of elevation of the tower becomes 60°. Find the height of the tower. [Answer: 94.8 m]

### Which questions and examples are student’s favourite from exercise 9.1 of class 10 Maths?

Examples 1, 2, 3 and Questions 8, 10, 12, 13 and 14 of exercise 9.1 (class 10 math) are student’s favourite questions because these questions are tricky to solve and understand. Students solve these questions without any difficult.

### In which questions exercise 9.1 of class 10th math, students face difficulty while solving?

While solving examples 4, 5, 6, 7 and Q6, 7, 8, 9, 10, 12, 13, 14, 15 and 16 of exercise 9.1 of class 10th math students face difficulty because these questions are little tough as compare to other questions and need proper attention while solving. Example 4 and questions 7, 8 are of same type.

### How much time students need to complete exercise 9.1 (chapter 9) of class 10th mathematics?

Students need at least 5 days to complete exercise 9.1 (chapter 9) of class 10th mathematics if they are giving at least 1-2 hours per day. This time also depends on student’s speed, efficiency and capability.

### Which question asked from exercise 9.1 of 10th Maths in Board exams?

Examples and questions can come from exercise 9.1 (chapter 9) of class 10th mathematics in Board exams. This exercise contains very good, interesting and logical questions and examples. The last three questions are very important from exam point of view.