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Aptitude Height and Distance Test Paper 1


1) Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse observed from the ships are 30° and 45° respectively. If the lighthouse is 100m high, find the distance between the two ships.

  1. 155.80 m
  2. 157.80 m
  3. 159. 80 m
  4. 161.80 m

The Correctoption is(B)

Answer with explanation:

Apti Height and distance10

Let AB be the height of lighthouse and C and D be the positions of the ships.

AB = 100 meters, ∠ACB = 45°, ∠ADB = 60°

Apti Height and distance11

AC = AB (100m)

AC = 100 m

Apti Height and distance12

Distance between ships, CD = AC + AD

Apti Height and distance13

2) A ladder is leaning against a wall. It makes a 60° angle with the wall. If the distance between foot of ladder and wall is 5.5 meters, find the length of the ladder.

  1. 9.5m
  2. 10m
  3. 10.5m
  4. 11m

The Correctoption is(D)

Answer with explanation:

Apti Height and distance14

Let BC be the wall and AC be the ladder.

∠BAC = 60° and AB = 5.5 meter

Apti Height and distance15

AC = 2 * AB

= 2 * 5.5 = 11 meters (Option D)


3) A man 1.5 meter tall is 30√3 meter away from a building. When he sees the top of building the angle of elevation is 30°. Find the height of the building?

  1. 31.5m
  2. 30 m
  3. 53.4m
  4. 48 m

The Correctoption is(A)

Answer with explanation:

Apti Height and distance16

Let AD be the man and BE the building.

Now draw a line DC so that DC is perpendicular to BE.

Now, BC = AD = 1.5 m

And, DC = AB = 30√3 m

Apti Height and distance17

Now, Height of building, BE = BC + EC

= 1.5 + 30 = 31.5 m (Option A)


4) The angle of elevation of the top of a tower at a point X is 30°. On walking 30 m towards the tower if the angle of elevation becomes 60° at point Y, find the height of the tower?

  1. 26 m
  2. 28 m
  3. 29 m
  4. 30 m

The Correctoption is(A)

Answer with explanation:

Apti Height and distance18

Let AB be the height of tower and XA be the distance between point X and base of tower.

Apti Height and distance19

XA = 3XA - 90

- 2XA = - 90

Apti Height and distance20

Put the value of XA in equation (1) to find AB (height of tower).

Apti Height and distance21

5) The tops of two poles are connected by a wire. The heights of the poles are 10 m and 14 m respectively. If the wire makes a 30° angle with the horizontal, find the length of the wire?

  1. 7 m
  2. 7.5m
  3. 8m
  4. 8.5m

The Correctoption is(C)

Answer with explanation:

Apti Height and distance22

Let AD and BE, be the poles of height 10 m and 14 m respectively.

DE is the wire of length = L

DC is parallel to AB so AD = BC = 10 m

So, CE = BE - BC = 14 - 10 = 4 m

Apti Height and distance23




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