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Aptitude Height and Distance Test Paper 4


16) The top and bottom of a flag on a building subtend angles of 60° and 30° respectively at a point B which is 48 meter away from the building. Find the height of the flag?

  1. 32 m
  2. 32 √3 m
  3. 18.49 m
  4. 16 m

The Correctoption is(B)

Answer with explanation:

Apti Height and distance47

Let height of building be AC = X and height of flag be CD = h.

Apti Height and distance48

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

Apti Height and distance49

17) From the top of a lighthouse which is 90 m above the sea, the angle of depression of a ship is 60°. How far is the ship from the lighthouse?

  1. 30 √3 m
  2. 30 m
  3. 17.34 m
  4. 20.5 m

The Correctoption is(A)

Answer with explanation:

Apti Height and distance50

Let the height of the lighthouse above sea be AC and it is given 90 m.

Ship is at point B so the distance between the base of lighthouse A and ship is AB.

Apti Height and distance51

18) The angles of elevation of the top of a tower from the top and bottom of a tree of height 15 m are 30° and 60° respectively. Find the height of the tower?

  1. 7.5 m
  2. 22.5 m
  3. 11.5 m
  4. 20 m

The Correctoption is(B)

Answer with explanation:

Apti Height and distance52

Let the CE be h meter.

Height of tree be AD = 15m

BE is the height of tower = BC + CE = 15 + h

AB = CD, let it is = X m

Apti Height and distance53

3 h = 15 + h

2 h = 15

h = 7.5 m

Height of tower = 15 + 7.5 = 22.5 m (Option B)


19) The distance between the tops of two trees is 16 m. If the heights of the trees are 20 m and 28 m respectively, find the horizontal distance between the two trees?

  1. 192 m
  2. √192 m
  3. 256 m
  4. √256 m

The Correctoption is(B)

Answer with explanation:

Apti Height and distance54

Let AE and BC be the heights of trees.

AE = 28 m

BC = 20 m

Horizontal distance between trees AB = DC

In Δ EDC, EC2 = ED2 + DC2 (Pythagoras theorem)

DC2 = EC2 - ED2

= 162 - 82

= 256 - 64

DC2 = 192

DC =√192 m (Option B)


20) There are two towers. The first tower of height 60 m casts a shadow of length 100m. At the same time if the second tower casts a shadow of length 140 m, find its height?

  1. 80 m
  2. 84 m
  3. 88 m
  4. 90 m

The Correctoption is(B)

Answer with explanation:

Apti Height and distance55

Let the height of the second tower = X

We know that the length of the shadow is directly proportional to the height of the tower.

Apti Height and distance56

X = 84 m (Option B)



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