### Quantitative Aptitude - Heights & Distances

#### Question - 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 $90°$

#### Question - 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

#### Question - 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

#### Question - 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

#### Question - 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

#### Question - 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
• E None of these

#### Question - 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

#### Question - 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

#### Question - 9

On the same side of a tower, two objects are located. Observed from the top of the tower, their angle of depression are $45°$ and $60°$. If the height of the tower is 150 m, the distance between the objects is :

• A 63.5 m
• B 76.9 m
• C 86.7 m
• D 90 m

#### Question - 10

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.