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?

32 m
32 √3 m
18.49 m
16 m

The Correctoption is(B)

Answer with explanation:

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

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

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?

30 √3 m
30 m
17.34 m
20.5 m

The Correctoption is(A)

Answer with explanation:

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.

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?

7.5 m
22.5 m
11.5 m
20 m

The Correctoption is(B)

Answer with explanation:

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

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?

192 m
√192 m
256 m
√256 m

The Correctoption is(B)

Answer with explanation:

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?