Height And Distance

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: A

Let AB be the tree and AC be its shadow.

Let ACB = .

Then,	AC	=	3 cot = 3
	AB

= 30°.

📖

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: C

Let AB be the tower.

Then, APB = 30° and AB = 100 m.

AB	= tan 30° =	1
AP	= tan 30° =	3

AP	= (AB x 3) m
	= 1003 m
	= (100 x 1.73) m
	= 173 m.

📖

An observer 1.6 m tall is 203 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: A

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	= tan 30° =	3

DE =	203	m = 20 m.
	3

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

📖

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: D

Let AB be the wall and BC be the ladder.

Then, ACB = 60° and AC = 4.6 m.

AC	= cos 60° =	1
BC	= cos 60° =	2

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

📖

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:

43 units

B:

8 units

C:

12 units

D:

Data inadequate

Answer: D

One of AB, AD and CD must have given.

So, the data is inadequate.

📖

Questions for: Height And Distance