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Aptitude Topics

Height and Distance

 
1

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

A.        173 m

B.        200 m

C.        273 m

D.        300 m

Answer: Option C

Explanation:

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

Then, AB = 100 m, ACB = 30° and ADB = 45°.

 

AB = tan 30° = 1          AC = AB x 3 = 1003 m.
AC 3

 

 

AB = tan 45° = 1          AD = AB = 100 m.
AD

 

 

 CD = (AC + AD) = (1003 + 100) m
  = 100(3 + 1)
  = (100 x 2.73) m
  = 273 m.

 

 
2

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?

A.        4√3 units

B.        8 units

C.        12 units

D.        Data inadequate

E.         None of these

Answer: Option D

Explanation:

One of AB, AD and CD must have given.

So, the data is inadequate.

 
3
 

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m

Answer: Option D

Explanation:

Let AB be the wall and BC be the ladder.

Then, ACB = 60° and AC = 4.6 m.

 

AC = cos 60° = 1
BC 2

 

 

 BC = 2 x AC
  = (2 x 4.6) m
  = 9.2 m.

 

 
4

An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

A.        21.6 m

B.        23.2 m

C.        24.72 m

 

D.        None of these

Answer: Option A

Explanation:

Let AB be the observer and CD be the tower.

Draw BE  CD.

Then, CE = AB = 1.6 m,

      BE = AC = 203 m.

 

DE = tan 30° = 1
BE 3

 

 

 DE = 203 m = 20 m.
3

 

 CD = CE + DE = (1.6 + 20) m = 21.6 m.

 
5
 

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:
A. 149 m
B. 156 m
C. 173 m
D. 200 m

Answer: Option C

Explanation:

Let AB be the tower.

Then, APB = 30° and AB = 100 m.

 

AB = tan 30° = 1
AP √3

 

 

 AP = (AB x √3 ) m
  = 100√3  m
  = (100 x 1.73) m
  = 173 m.

 

 
6
6. 

The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:
A. 30°
B. 45°
C. 60°
D. 90°

Answer: Option A

Explanation:

Let AB be the tree and AC be its shadow.

Let ACB = .

 

Then, AC = √3           cot  = √3
AB

 

  = 30°.