Height and Distance
Height and Distance
Angle of Elevation:
The angle which is above the horizontal line and the condition from which the angle is formed by the line of sight with the horizontal line is called angle of elevation.
In the given figure, the object is at a higher level than the observer's eye. So, ∠ACB = θ is the angle of elevation.
Angle of Depression:
The angle which is below the horizontal line and the condition from which the angle is formed with the horizontal line is called angle of depression.
Let, In the given figure, the object is at a lower level than the observer's eye. Therefore ∠PQR = θ is the angle of depression.
 The angle which is above the horizontal line and the condition from which the angle is formed by the line of sight with the horizontal line is called angle of elevation.
 The angle which is below the horizontal line and the condition from which the angle is formed with the horizontal line is called angle of depression.

A man is walking along a straight road. He notices the top of a tower subtending an angle A = 60^{o} with the ground at the point where he is standing. If the height of the tower is h = 35 m, then what is the distance (in meters) of the man from the tower?
25m
20.21m
25.2m
22.02m

A little boy is flying a kite. The string of the kite makes an angle of 30^{o} with the ground. If the height of the kite is h = 12 m, find the length (in meters) of the string that the boy has used.
26m
24m
25m
19m

Two towers face each other separated by a distance d = 30 m. As seen from the top of the first tower, the angle of depression of the second tower's base is 60^{o} and that of the top is 30^{o}. What is the height (in meters) of the second tower?
24.26m
34.64m
25.25m
36.20m

A ship of height h = 18 m is sighted from a lighthouse. From the top of the lighthouse, the angle of depression to the top of the mast and the base of the ship equal 30^{o} and 45^{o} respectively. How far is the ship from the lighthouse (in meters)?
45.45m
42.59m
46.16m
44.43m

Two men on opposite sides of a TV tower of height 32 m notice the angle of elevation of the top of this tower to be 45^{o} and 60^{o} respectively. Find the distance (in meters) between the two men.
45.23m
50.48m
49.21m
52.41m

Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30^{o} and 60^{o}respectively. If the height of the building is known to be h = 90 m, find the distance (in meters) between the two men.
95m
102.54m
100m
103.92m

A pole of height h = 40 ft has a shadow of length l = 23.09 ft at a particular instant of time. Find the angle of elevation (in degrees) of the sun at this point of time.
62
80
65
60

You are stationed at a radar base and you observe an unidentified plane at an altitude h = 4000 m flying towards your radar base at an angle of elevation = 30^{o}. After exactly one minute, your radar sweep reveals that the plane is now at an angle of elevation = 60^{o} maintaining the same altitude. What is the speed (in m/s) of the plane?
76.98m/s
78m/s
88.25m/s
96m/s

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
200 m
273 m
300 m
173 m

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 45º. What is the distance between the base of the tower and the point P?
12 units
9 units
Data inadequate
3(sqrt{3}) units

From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 200 m high, the distance of point P from the foot of the tower is:
346 m
312 m
298 m
400 m

The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
60°
45°
30°
None of these

An observer 2 m tall is 10(sqrt{3}) m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:
14 m
12 m
10 m
None of these

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:
24.8 m
14.8 m
6.2 m
12.4 m

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:
64.2 m
54.6 m
62.2 m
52.2 m

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