# Height and Distance Questions for Competitive Exams

*NEW*

Height and distance are one of the important parts of the mathematics subject. Height is the measurement in the vertical direction of any object, such as our height. Similarly, the measurement of anything from top to bottom is called height. On the other, the distance between objects from one object to another is called distance. As if something is 100 meters away from a certain point or 1 km away, it is called distance. This topic is a must for those candidates who are preparing for competitive exams like SSC, UPSC, Banking, Defense. 2 to 3 questions are asked often from this topic in government examinations.

So let's start practice with height and distance questions below:

## Height and Distance Questions

** Q : **

**A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60 ° with the ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30° with ground. How much did the ladder slip? **

(A) 30 (√3-1) ft

(B) 18 (√3-1) ft

(C) 10 (√3-1) ft

(D) 20 (√3-1) ft

Correct Answer : C

**Q :**

A helicopter, at an altitude of 1500 metre, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30° respectively. Distance between the two ships, in metre is

(A) 500 √3

(B) $${500\over√3}m$$

(C) 100√3

(D) $${1000\over√3}m$$

Correct Answer : C

**Q :**

A pilot in an aeroplane at an altitude of 200 m observes two points lying on either side of a river. If the angles of depression of the two points be 45 ° and 60 °, then the width of the river is

(A) 400√3m

(B) $${400\over√3}m $$

(C) $$200+{200\over√3}m $$

(D) $$200-{200\over√3}m $$

Correct Answer : C

**Q :**

An earthing wire connected to the top of an electricity pole has its other end inside the ground. The foot of the wire is 1.5 m away from the pole and the wire is making an angle of 60° with the level of the ground. Determine the height of pole.

(A) √3

(B) $${√3\over2}m$$

(C) $${3√3\over2}m$$

(D) 3 m

Correct Answer : C

**Q :**

A boat is moving away from an observation tower. It makes an angle of depression of 60 ° with an observer's eye when at a distance of 50 m from the tower. After 8 sec, the angle of depression becomes 30 °. By assuming that it is running in still water, the approximate speed of the boat is

(A) 45 km/h

(B) 50 km/h

(C) 33 km/h

(D) 42 km/h

Correct Answer : A

**Q :**

From a point P on the ground the angle of elevation of the top of a 10m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45^{0}. Find the length of the flagstaff (Take √3 = 1.732)

(A) 10 √3 m

(B) 7.32 m

(C) 10 (√30+2) m

(D) 10 (√30+1) m

Correct Answer : B

**Q :**

The distance between two parallel poles is 40√3 m. The angle of depression of the top of the second pole, when seen from the top of first pole, is 30 °. What will be the height of second tower if the first pole is 100m long?

(A) 35 √3

(B) 60 m

(C) 50 √3 m

(D) 80 m

Correct Answer : B

**Q :**

An Aeroplan flying horizontally at a height of 3 km. Above the ground is observed at a certain point on earth to subtend an angle of 60 °. After 15 sec flight, its angle of elevation is changed to 30 °. The speed of the Aeroplan (taking √3 = 1.732)

(A) 235.93 m/sec.

(B) 236.25 m/sec.

(C) 230.63 m/sec.

(D) 230.93 m/sec.

Correct Answer : D

**Q :**

The shadow of a tower standing on a level plane is found to be 30 metre longer when the Sun's altitude changes from 60 ° to 45 °. The height of the tower is

(A) 15 (√3-1) m

(B) 15 (3-√3) m

(C) 15 (3+√3) m

(D) 15 (3-√3) m

Correct Answer : C

**Q :**

The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45 ° to 30 °. Then the height of the tower is

(A) 30(√3+1) m

(B) 30(√3-1) m

(C) 20(√3+1) m

(D) 24(√3+1) m

Correct Answer : A