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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 30Â° and 45Â° respectively. If the lighthouse is 100m high, find the distance between the two ships.

- 155.80 m
- 157.80 m
- 159. 80 m
- 161.80 m

The Correctoption is(B)

**Answer with explanation:**

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

AB = 100 meters, âˆ ACB = 45Â°, âˆ ADB = 60Â°

AC = AB (100m)

AC = 100 m

Distance between ships, CD = AC + AD

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

- 9.5m
- 10m
- 10.5m
- 11m

The Correctoption is(D)

**Answer with explanation:**

Let BC be the wall and AC be the ladder.

âˆ BAC = 60Â° and AB = 5.5 meter

AC = 2 * AB

= 2 * 5.5 = 11 meters (Option D)

3) A man 1.5 meter tall is 30âˆš3 meter away from a building. When he sees the top of building the angle of elevation is 30Â°. Find the height of the building?

- 31.5m
- 30 m
- 53.4m
- 48 m

The Correctoption is(A)

**Answer with explanation:**

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 = 30âˆš3 m

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 30Â°. On walking 30 m towards the tower if the angle of elevation becomes 60Â° at point Y, find the height of the tower?

- 26 m
- 28 m
- 29 m
- 30 m

The Correctoption is(A)

**Answer with explanation:**

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

XA = 3XA â€“ 90

â€“ 2XA = â€“ 90

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

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 30Â° angle with the horizontal, find the length of the wire?

- 7 m
- 7.5m
- 8m
- 8.5m

The Correctoption is(C)

**Answer with explanation:**

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 â€“ BC = 14 â€“ 10 = 4 m

Height and Distance Aptitude Test Paper 3

Height and Distance Aptitude Test Paper 4