## Important Questions for Class 10 Maths Some Applications of Trigonometry

1. The ratio of the height of a tower and the length of its shadow on the ground is

3 : 1 . What is the angle of elevation of the sun?

2. A boy standing on a horizontal plane finds a bird flying at a distance of 100m from

him at an elevation of 30^{o}. A girl standing on the roof of 20m high building find the

angle of elevation of the same bird to be 45^{o}.Both the boy and girl are on opposite

sides of the bird. Find the distance of the bird from the girl.

3. A man rowing a motorboat away from a lighthouse 150 m high takes 2 minutes to change the angle of elevation of the top of lighthouse from 45^{0} to 30^{0}. Find the speed of the boat. ( use 3 = 1.732)

4. The angle of elevation of a cloud from a point 60m above a lake is 30 degree, and the angle of depression of the reflection of the cloud in the lake is 60 degree. Find the height of the cloud from the surface of the lake.

5. From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter, hovering at some height vertically over the top of the building are 30⁰ and 60⁰ respectively. Find the height of the helicopter above the ground.

6. The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of a tower to the foot of hill is 30⁰.If tower is 50 m high, find height of the hill.

7. A pole 5 metre high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60⁰ and the angle of depression of the point A from the top of the tower is 45⁰.Find the height of the tower.(use √3=1.73)

8. The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60^{0}. Find the angle of elevation of the sun of the longer shadow.

9. 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 45⁰. 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 degree. Find the speed of the flying of the bird.

10. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30⁰ and 60⁰ respectively. Find the distance between the two planes at that instant.

11`.Two poles are 25 metre and 15 metre high and the line joining their tops makes an angle of 45⁰ with the horizontal. Determine the distance between these poles.

12. A man on the deck of a ship, 12m above water level, observes that the angle of elevation of the top of the cliff is 60^{0} and the angle of depression of the base of the cliff is 30^{0}. Find the distance of the cliff from the ship and the height of the cliff.

** CASE STUDY**: A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that

**India Gate**, official name

**Delhi Memorial**, originally called

**All-India War Memorial**, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The teacher also said that India Gate, which is located at the eastern end of the Kartavya path (formerly called the Kingsway), is about 138 feet (42 metres) in height.

- What is the angle of elevation if they are standing at a distance of 42m away from the monument?
- They want to see the tower at an angle of 60. So, they want to know the distance where they should stand and hence find the distance.
- If the altitude of the Sun is at 60, then find the height of the vertical tower that will cast a shadow of length 20 m
- The ratio of the length of a rod and its shadow is 1:1. Then find the angle of elevation of the Sun.
- Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 1.2
- Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 2.2
- Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/
- Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**

Important Questions for Class 10 Maths Some Applications of Trigonometry

Important Questions for Class 10 Maths Some Applications of Trigonometry

Important Questions for Class 10 Maths Some Applications of Trigonometry

Important Questions for Class 10 Maths Some Applications of Trigonometry

Important Questions for Class 10 Maths Some Applications of Trigonometry

Important Questions for Class 10 Maths Some Applications of Trigonometry