1. Heights and distance tutorial

2. Q.1 The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 5 m away from the wall. What is the length of the ladder?
5 m
5√3 m
5√3 / 3 m
10 m d

3. Q.2 The angle of elevation of the top of the tower from a point on the ground is tan−1(3/5). If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?
9 m
18 m
15 m
12 m d

4. Q. 3 A little boy is flying a kite
Q.3 A little boy is flying a kite. The string of the kite makes an angle of 30o with the ground. If the height of the kite is h = 9 m, then find the length (in meters) of the string that the boy has used.
6√3 m
12√3 m
18 m
18√3 m c

5. Q.4 Two men on opposite sides of a TV tower of height 20 m notice the angle of elevation of the top of this tower to be 45o and 60o respectively. Find the distance (in meters) between the two men.
20√3 m
20√3 / 3 m
20 (√3 – 1 /√3) m
20 (√3 + 1 /√3) m d

6. Q. 5 On the same side of a tower, two objects are located
Q.5 On the same side of a tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 600 m, the distance between the objects is approximately equal to :
572 m
384 m
188 m
254 m d

7. Q.6 A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?
9 m
10.40 m
15.57 m
12 m a

8. Q.7 From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?
52 m
50 m
66.67 m
33.33 m c

9. Q.8 The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 40 m towards the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:
50.2 m
69.2 m
52.2 m
78.6 m b

10. Q.9 A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
26.28 km/hr
42.42 km/hr
4.22 km/hr
51.25 km/hr a

11. Q.10 A man on the top of a vertical observation tower observers a car moving at a uniform speed coming directly towards it. If it takes 8 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower?
8 min 17 second
10 min 57 second
14 min 34 second
12 min 23 second

12. Both will pick it at the same time Cannot be determined
Q.11 Two crows A and B are sitting at a height of 15 m and 10 m respectively in two different trees vertically opposite to each other. They view a pizza on the ground at an angle of depression 45° and 60° respectively. They start flying towards it at the same time and at the same speed along the shortest path to pick up the pizza. Which bird will succeed in it?
First bird
Second bird
Both will pick it at the same time
Cannot be determined a

13. Thank you