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SSC Quantitative Aptitude - Heights and Distances Important Questions

Quantitative Aptitude - Heights and Distances

Exam Duration: 45 Mins Total Questions : 10

1 )

The angle of elevation of the sun, when the length of the shadow of a tree is \(\sqrt3\) times the height of the tree is :

(a)
\(30°\)
(b)
\(45°\)
(c)
\(60°\)
(d)
\(90°\)

2 )

From a point P on a level ground, the angle of elevation of the top of a 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

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

4 )

An observer 1.6 m tall is \(20\sqrt3\) 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

5 )

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two 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

6 )

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 elevation becomes \(60°\). What is the distance between the base of the tower and the point P ?

(a)
\(4\sqrt3\) units
(b)
8 units
(c)
12 units
(d)
Data inadequate
(e)
None of these

7 )

The angle of elevation of the top of a tower from a certain point is \(30°\). If the observer moves 20 m towards the tower, the angle of elevation of the top of the tower increases by \(15°\). The height of the tower is :

(a)
17.3 m
(b)
21.9 m
(c)
27.3 m
(d)
30 m

8 )

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of \(45°\) with the man's eye when at a distance of 60 metres from the tower. After 5 seconds, the angle of depression becomes \(30°\). What is the approximate speed of the boat, assuming that it is running in still water ?

(a)
32 kmph
(b)
36 kmph
(c)
38 kmph
(d)
40 kmph
(e)
42 kmph

9 )

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from \(30°\) to \(45°\), how soon after this will the car reach the observation tower ?

(a)
14 min. 35 sec
(b)
15 min. 49 sec.
(c)
16 min. 23 sec.
(d)
18 min. 5 sec.

10 )

The top of a 15 metre high tower makes an angle of elevation of \(60°\) with the bottom of an electric pole and angle of elevation of \(30°\) with the top of the pole. What is the height of the electric pole ?