NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 Some Applications of Trigonometry in Hindi and English 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 2022-23. All NCERT Solutions and Offline Apps 2022-23 are free use online for all CBSE and UP Board High School students who are using NCERT Books 2022-23 for their March 2021 exams. Download Offline apps and PDF Solutions free for offline use.

Class: 10 | Maths Solutions |

Chapter 9: | Exercise 9.1 |

Medium: | English and Hindi Medium |

### 10 Maths Chapter 9 Exercise 9.1 Solutions

NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 Some Applications of Trigonometry â€“ Height and Distance questions in PDF form to free download and for online use also, updated for new academic session 2022-23. Visit to Class 10 Maths Chapter 9 main page for other exercises whether download or online study.

#### Class 10 Maths Chapter 9 All Questions in Videos

#### 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 60Â° and 45Â° 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 30Â° and the angle of depression of its reflection of the cloud in the lake is 60Â°. 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 45Â°. 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 30Â°. 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 60Â° and the angle of depression of the foot of the tower is 30Â°. 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 30Â°. A girl, standing on the roof of 20 m high building, finds the angle of elevation of the same bird to be 45Â°. Both the boy and girl are on the opposite sides of the bird. Find the distance of bird from the girl. [Answer: 30âˆš2 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 30Â°. [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 30Â° and 45Â°. 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 60Â° with the horizontal. Find the height of the kite above the ground. (Assume string to be tight). [Answer: 75âˆš3]

5. The upper part of a tree broken over by the wind makes an angle of 30Â° 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 45Â°. 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 45Â° to 30Â°. 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 45Â° and 60Â°, find the width of the river. [Answer: 315.8 m]

3. A fire in a building â€˜Bâ€™ 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 60Â° to the road, and Q observes, that it is at an angle of 45Â° 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 60Â°. After some time, the angle of elevation reduces to 30Â°. Find the distance travelled by the balloon. [Answer: 58âˆš3 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 30Â° to 60Â°. 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 30Â° and 60Â° 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 60Â° and angle of depression the bottom of a hill as 30Â°. 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 45Â° and 30Â° respectively. Find the height of the tower. [Answer: 9.6 m]

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

### Which questions and examples are studentâ€™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 studentâ€™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 studentâ€™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.