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Aptitude Height and Distance Test Paper 3


11) Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

  1. 30.8 m
  2. 60 m
  3. 76.8 m
  4. 40.5 m

The Correctoption is(A)

Answer with explanation:

Apti Height and distance34

Le t the height of the second building AD be h.

EC = 100 - h

DC = AB = 40

Apti Height and distance35

100 -h = 40 * √3

- h = -100 + 40 * 1.73

- h = -100 + 69.2

h = 30.8 m ( Option A)


12) The angle of elevation of the top of a tower of height h meter at point Q is θ. If the distance between point Q and base of the tower is equal to the height of the tower, find the value of θ?

  1. 60°
  2. 30°
  3. 45°
  4. any acute angle

The Correctoption is(C)

Answer with explanation:

Apti Height and distance36

Let the height of tower PR be h.

PQ = h as point Q is at a distance of h meter from the base of tower.

Apti Height and distance37

tan θ=1

tanθ= 45° ( Option C)


13) The shadow of a pole of height 3 meter when the angle of elevation of the sun is 60°, is

Apti Height and distance38

The Correctoption is(B)

Answer with explanation:

Apti Height and distance39

Let the length of the shadow be AB = X meter.

Height of tower, AC = 3 meter

Apti Height and distance40

X = √3 m (Option B)


14) A kite is flown with a thread of length 200 meter. The thread is fully stretched and makes an angle of 60° with the horizontal, find the height of the kite above the ground.

  1. 173 m
  2. 100 m
  3. 346 m
  4. 141 m

The Correctoption is(A)

Answer with explanation:

Apti Height and distance41

Let height of the kite above the ground be AC = h.

Length of thread, BC = 200 m

Apti Height and distance42

= 100 * √l3

= 100 * 1.73

= 173 m ( Option A)


15) A plane is flying over two villages which are 4 km apart. If at an instant the angles of depression of these villages from the plane are 45° and 60° respectively, find the height of the plane at that instant?

Apti Height and distance43

The Correctoption is(4)

Answer with explanation:

Apti Height and distance44

Let the plane is at point D and villages at points B and C respectively.

Let the height of the plane be AD = h.

Apti Height and distance45

h = X + 4 ..................(2)

Put value of X in equation (2) from equation (1)

Apti Height and distance46




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