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 **