CBSE Class 10 Mathematics Some Application Of Trigonometry Notes

Chapter 9: Some Application of Trigonometry

Top Definitions

1. The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

2. The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object.

3. The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object.

4. Pythagoras theorem: In a right triangle, square of the hypotenuse is equal to the sum of the square of the other two sides.

5. Ratio of the sides of the right triangle with respect to the acute angles is called trigonometric ratios of the angle.

Top Concepts

1. The height or length of an object or the distance between two distant objects can be determined by the help of trigonometric ratios.

2. When any two sides of a right triangle are given, its third side can be obtained by using Pythagoras theorem.

3. Angle measured in anticlockwise direction is taken as positive angle.

4. Angle measured in clockwise direction is taken as negative angle.

5. The values of the trigonometric ratios of an angle do not vary with the length of the sides of the triangle, if the angles remain the same.

6. Each trigonometric ratio is a real number. It has no unit.

7. Only symbol cosine, sine, tangent, cotangent, sec and cosec has no meaning.

8. The two heights above and below the ground level in case of reflection.

More MCQs for NCERT Class 10 Mathematics Application Of Trigonometry...

1. If the angle of elevation of cloud from a point ‘h’ meters above a lake is α and the angle of depression of its reflection in the lake is β then the height of the cloud is=?

Answer :  (A)

2. From an aero plane vertically above a staright horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aero plane are observed to be α and β . The height of the aero plane above the road is

Answer :  (B)

3. The stations due south of a tower, which learns towards north are at distances ‘a’ and ‘b’ from its foot. If α and β be the elevations of the top of the tower from the situation, then its inclination θ’ to the horizontal given by

Answer :  (A)

4. The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α . On advancing ‘p’ meters towards the foot of the tower, the angle of elevation becomes β . The height ‘h’ of the tower is given by h=?

Answer :  (B)

5. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 0 30 . A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. The distance of the bird from the girl is

A) 20.42 m B) 42.42 m C) 42.32 m D) None of these

Answer :  (B)

6. From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the opposite side of the street are α and β respectively. The height of the opposite house is =?

A) x(1+ tanα.cotβ ) B) x(1+ tanα.cotβ ) C) x(1+sinα.cotβ ) D) None of these

Answer :  (A)

7. Two ships are sailing in the sea on either side of a lighthouse; The angles of depression of two ships as observed from the lighthouse are 0 60 and 0 45 respectively. If the distance between the ships is 200( 1+√3/√3) meters, then the

A) 150 m B) 200m C) 250 m D) None of these

Answer :  (B)

8. A round balloon of radius ‘a’ subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Ø . Then the height of the center of the balloon.

A) asinθ.cosec4 B) asinθ .sin∅ C) a cosec 4/2 sin∅ D) None of these

Answer :  (C)

9. The angle of elevation of a jet fighter from a point A on the ground is 0 60 . After a fight of 15 seconds, the angle of elevation changes to 300. If the jet is flying at a speed of 720 km/hr then constant height at which the jet is flying. ( Use 3 π1.732

A) 2598 m B) 2600 m C) 2500 m D) 2550 m

Answer : (A)

10. The angle of elevation of the top of the tower standing on a horizontal plane from a point A is α.After walking a Distance ‘d’ towards the foot of the tower the angle of elevation is found to be β. Then height of the tower is?

A) cotα - cotβ
B) cotα + cotβ
C) sinα + sinβ
D)NONE

Answer :  (A)

11. A man on a top of tower observes a truck at an angle of depression α where tan α 1/√5 and sees that it is moving towards the base og the tower. Ten minutes later, the angle of depression of the truck is found to be β where tan β =√5 , if the truck is moving at a uniform speed, determine how much more time it will take to reach the base of the tower.

A) 100 sec B) 200 sec C) 150 sec D) 250 sec

Answer :  (C)

12. A ladder sets against a wall at an angle α to the horizontal. If the root is pulled away from the wall through a distance of ‘a’, so that is slides a distance ‘b’ down the wall making an angle β with the horizontal. Then cosα - cosβ /sinβ - sin α =?

A) (b/a)

B) (a/b)

C) (2b/a)

D) (2a/b)

Answer :  (B)

13. Two stations due south of a leaning tower which leans towards the north are at distance a and b from its foot. If α ,β be the elevations of the top of the tower from these stations, prove that its inclination Ø is given by

A) cos∅ B) sin∅ C) cot∅ D) tan∅

Answer : (C)

14. In figure, what are the angles of depression from the observing positions  O₁ and  O₂ of the object at A?

Answer :  (A)

Please click the link below to download pdf file for CBSE Class 10 Mathematics - Some Application of Trigonometry Concepts.