Practice Questions: Some Applications of Trigonometry | Mathematics (Maths) Class 10 PDF Download

Questions

1. 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 is 60°. Find the height of the tower.

2. The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. 

3.  If the length of the shadow of a tree is decreasing then the angle of elevation is _________________________.

4. 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) Do not change
(d) None of the above

5. If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is?

6. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called ________________.

7. An observer 1.5 m tall is 28.5 m away from a tower of height 30 m. Find the angle of elevation of the top of tower from his eye.

8. The tops of two poles of height 16 m and 12 m are connected by a wire, the wire makes angle of 30° with the horizontal, find length of wire.

9. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.

10. There are two poles, one each on either bank of a river, just opposite to each other. One pole is 60 m high. From the top of this pole, the angles of depression of the top and the foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.

11. 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°.

12. The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the light house.

13. 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
(a) also get doubled
(b) will get halved
(c) will be less than 60 degree
(d) None of these

14. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill. 

15. Two poles of equal heights are standing opposite to each other on either side of the road, which is 100 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles.

Answers

1. 20√3 m

2. The height of the tower is 10(√3 + 1) m.

3. Increasing

4. (c) Do not change

5. 60°

6. Angle of elevation

7. 45°

8. Length of the wire = 8m

9. The height of the hill is 40m.

10. Width of river = 20√3 m and Height of the other pole = 40 m.

11. The height of the vertical pole is 10 m.

12. ∴ Height of the light house = 273 m

13. (c) will be less than 60 degree

14. The distance of the hill from the ship is 17.3 m and the height of the hill is 40 m.

15. Height of the poles = = 43.25 m