A vertical pole of length 6 m casts shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Let A B be the length of the pole and B C be its shadow , then A B = 6 m and B C = 4 m Also let P Q be the tower and Q R be its shadow Assume the length of P Q as x m . In △ A B C and △ P Q R , we have ∠ A B C = ∠ P Q R = 90 ° ∠ A C B = ∠ P R Q --[as at the same time both cast the shadow, so their angle with the ground will be same] ∴ △ A B C ~ △ P Q R --[ A A similarity] ⇒ A B B C = P Q Q R --[as the sides of similar triangles are proportional] ⇒ 6 4 = x 28 ⇒ x = 6 × 28 4 ⇒ x = 42 m Thus, the height of tower is 42 m .

An observer 1 . 5 m tall is 28 . 5 m away from a chimney. The angle of elevation of the top of the chimney from his eyes is 45 ° . What is the height of the chimney?

Given: Height of chimney C D = B E = 1 . 5 m . Distance between observer and chimney B C = D E = 28 . 5 m . Angle of elevation ∠ C = 45 ° . From △ A B C , we have ⇒ tan C = A B B C ⇒ tan 45 ° = A B 28 . 5 ⇒ 1 = A B 28 . 5 ∴ A B = 28 . 5 m . Total height of the chimney, A E = A B + B E = 28 . 5 + 1 . 5 = 30 m Hence, the height of the chimney is 30 m .

EASY

10th Madhya Pradesh Board

IMPORTANT

Earn 100

Define Angle of Elevation.

Important Questions on Some Applications of Trigonometry

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2018>Q 1

Define Angle of Elevation.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2018>Q 2

At a point

25 m

away from the foot of a building, the angle of elevation of the top of the building is

45 °

. Find the height of the building.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2018>Q 3

From the top of

60 m

high light house, the angle of depression of the ship is

60 °

. Find the distance between the ship and foot of the light house.

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2019>Q 4

The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal, when we lower our head to look at the object.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2019>Q 5

From a point

P

on the ground the angle of elevation of the top of a

10

meter tall building is

30 °

. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from

P

45 °

. Find the length of the flagstaff and the distance of the building from the point

P

.(You may take

\sqrt{3} = 1.732

)

HARD

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2019>Q 6

The angle of depression of the top and the bottom of an

8 m

tall building from the top of a multi-storeyed building is

30 °

and

45 °

respectively. Find the height of the multi-storeyed building and distance between the two buildings.

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2020>Q 7

Write the definition of the Line of sight.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Some Applications of Trigonometry>Madhya Pradesh Board-2020>Q 9

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 °

Define Angle of Elevation.

Important Questions on Some Applications of Trigonometry

Learn and Prepare for any exam you want !