Heights and Distances : Class X Model Questions

Heights and Distances : Class X Model Questions
 

1. The angle of elevation of the top of a tower, from a point on the ground and at a distance of 150 m from its foot,

is 30°. Find the height of the tower correct to one decimal place.

2. From a point P on the level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high,

how far is P from the foot of tower?

3. A kite is flying at a height of 75 meters from the level ground, attached to a string inclined at 60° to the horizontal. Find the length of the string to the nearest meter.

4. If the length of a shadow cast by a pole be underroot(3) times the length of the pole, find the angle of elevation of the sun.

5. A vertical tower is 20 m high. A man at some distance from the tower knows that the cosine of the angle of

elevation of the top of the tower is 0·53. How far is he standing from the foot of the tower?

[Hint. If is the angle of elevation, then cos = ·53 => = 58°]

6. (a) From a boat 300 meters away from a vertical cliff, the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are 55° 40' and 54°20' respectively. Find the height of the pillar correct to the nearest meter.

(b) From a man M, the angle of elevation of the top of a tree is 44°. What is the angle of elevation from the man

of a bird perched half way up the tree?

7. The upper part of a tree broken by wind, falls to the ground without being detached. The top of the broken part

touches the ground at an angle of 38° 30' at a point 6 m from the foot of the tree. Calculate

(i) the height at which the tree is broken.

(ii) the original height of the tree correct to two decimal places.

8. The angle of elevation of the top of a tower from a point A (on the ground) is 30°. On walking 50 m towards the tower, the angle of elevation is found to be 60°. Calculate

(i) the height of the tower (correct to one decimal place).(ii) the distance of the tower from A.

9. From the top of a church spire 96 m high the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = 1/4 and tan y° = 1/7. Calculate thedistance between the vehicles.