Define Angle of Elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation. The three terms related to the angle of elevation are: 1 . Angle 2 . Horizontal Line 3 . Line of sight Angle : If two rays or two line segments meet at a common endpoint, then the point is known as the vertex. Two straight lines meet at a common point is said to form an angle. Angle play an important role, and some other definitions of angle are: The angle is a gap in between two lines which connect on one side. The angles are measured in degrees. Horizontal Line : A straight line on the coordinate flat surface where all points on the line have the same y -coordinate. The angle and horizontal line combine to form the angle of elevation. Line of Sight : The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.

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.

Let A B is a 60 m high light-house and a ship is at the point C In △ A B C , AB = 60 m tan 60 ° = AB BC ⇒ 3 = 60 BC ⇒ BC = 60 3 m ⇒ BC = 3 × 20 3 m ⇒ BC = 20 3 m Hence, the distance between the ship and foot of the light house 20 3 m .

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.

Consider the figure below, Let A B represent the height of the building. In △ A B C , tan 45 ° = AB BC ⇒ 1 = AB 25 ⇒ AB = 25 m Hence, the height of the building is 25 m .

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.

Given: Height of building E D = B C = 8 m , angle of depressions (by alternate interior angle) ∠ E = 30 ° , ∠ D = 45 ° . Let the height of the multi storey building be A C and let A B = y and the distance between two buildings C D = B E be x . Consider △ A B E , ⇒ tan 30 ° = A B B E ⇒ 1 3 = y x ⇒ x = y 3 . . . . ( i ) Consider △ A C D , ⇒ tan 45 ° = A C C D ⇒ 1 = A B + B C x ⇒ x = y + 8 . . . . ( ii ) Now, equating equation ( i ) and ( ii ) , we have ⇒ y + 8 = y 3 ⇒ y 3 - y = 8 ⇒ y = 8 3 - 1 Rationalizing the denominator, we get ⇒ y = 8 3 - 1 × 3 + 1 3 + 1 ⇒ y = 8 3 + 1 2 ∴ y = 4 3 + 1 m ⇒ A C = A B + B C = y + 8 = 4 3 + 1 + 8 = 4 3 + 12 = 4 3 + 3 m . Since, x = y + 8 . ⇒ x = 4 3 + 1 + 8 = 4 3 + 4 + 8 = 4 3 + 12 = 4 3 + 3 m . Therefore, the height of the multi storey building is 4 3 + 3 m and their distance is 4 3 + 3 m .

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 is 45 ° . Find the length of the flagstaff and the distance of the building from the point P .(You may take 3 = 1 . 732 )

Given, RQ = 10 m (Height) SR = x m (length of flag staff) PQ = y m (distance from point P ) ∠ RPQ = 30 ° and ∠ SPQ = 45 ° In ∆ RQP RQ PQ = tan 30 ° ⇒ 10 y = 1 3 ⇒ y = 10 3 m (i) In ∆ SQP SQ PQ = tan 45 ° ⇒ 10 + y y = 1 ⇒ 10 + x = y From (i), we have 10 + x = 10 3 x = 10 3 - 10 x = 10 ( 3 - 1 ) m Hence, length of flag staff is 10 ( 3 - 1 ) m and distance of the building from the point P is 10 3 m .

E M B I B E

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

EASY

10th Madhya Pradesh Board

IMPORTANT

Earn 100

Write the definition of the Line of sight.

Important Questions on Some Applications of Trigonometry

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 8

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?

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