Class 10 – Maths

Chapter – 9 Applications of trigonometry

Quiz  (1- Mark Questions)

Q-1 The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

(a) 10√3 m             (b) 15√3 m

(c) 12√3 m              (d) 36 m

Ans – (a) 10√3 m

Q-2 If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:

(a) 60°        (b) 45°

(c) 30°         (d) 90°

(a) 60°

Q-3 The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:

(a) Angle of elevation               (b) Angle of depression

(c) No such angle is formed    (d) None of the above

Ans – (a) Angle of elevation

Q-4 From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower (in m) standing straight is:

(a) 15√3                    (b) 10√3

(c) 12√3                     (d) 20√3

Ans – (a) 15√3

Q-5 The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be

(a) Angle of elevation               (b) Angle of depression

(c) Line of sight                           (d) None of the above

Ans – (b) Angle of depression

Q-6 When the shadow of a pole h metres high is √3h metres long, the angle of elevation of the Sun is

(a) 30°                (b) 60°           (c) 45°                (d) 15°

Ans – (a) 30°

Q-7 The angle of depression of an object on the ground, from the top of a 25 m high tower is 30°. The distance of the object from the base of tower is

(a) 25√3 m        (b) 50√3 m     (c) 75√3 m           (d) 50 m

Ans – (a) 25√3 m

Q-8 The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. The height of the tower is –

(a) 40√3 m           (b) 20√3              (c) 20 m         (d) 15√3 m

Ans – (b) 20√3

Q-9 If the angles of elevation of the top of a tower from two points at the distance of a m and b m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is

(a) √(a/b)        (b) √ab        (c) √(a + b)          (d) √(a – b)

Ans – (b) √ab

Q-10 From a point on a bridge across a river the angle of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 30 m from the banks, the width of the river is

(a) 30(1 + √3) m     (b) 30(√3 – 1) m    (c) 30√3 m     (d) 60√3 m

Ans – (a) 30(1 + √3) m

Q-11 The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. The angle of elevation of the Sun is

(a) 30°            (b) 45°           (c) 60°           (d) 75°

Ans – (c) 60°

Q-12 The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will be

(a) Greater than 60°     (b) Equal to 30°     (c) Less than 60°  (d) Equal to 60°

Ans – (c) Less than 60°

Q-13 If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:

(a) Increases         (b) Decreases        (c) Does not change (d) None of the above

Ans – (c) does not change

Q-14 The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

(a) 10√3 m       (b) 15√3 m        (c) 12√3 m        (d) 36 m

Ans – (a) 10√3 m

Q-15 From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower (in m) standing straight is:

(a) 15√3       (b) 10√3   (c) 12√3      (d) 20√3

Ans – (a) 15√3