Quantitative Aptitude HEIGHT & DISTANCE for SBI CLERK & PO

Height & Distance is an important topic of trigonometry from which questions are expected in banking as well as SSC exams. The concept of Height & Distance is not much tricky but you should be aware with the values of all trigonometric ratios at different angles.

Let us understand the concept of Height & Distance with the help of some examples:

Ques: The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6m away from the wall. The length of the ladder is:

Sol: Let AB be the wall and BC be the ladder.

Then, ےACB = 60º and AC = 4.6 m

AC / BC = cos 60⁰ = 1/2

So, BC = 2 * AC

= 2 * 4.6 = 9.2m

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Ques: From a point P on level ground, the angle of elevation of the top of the tower is 30º. If the tower is100 m high, the distance of point P from the foot of the tower is:

Sol: Let AB be the tower.

Then, ےAPB = 30⁰& AB = 100m

AB / AP = tan 30⁰= 1/√3

So, AP = AB * √3

= 100 * √3

= 100√3 m.

Ques: 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 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

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

Then, AB = 100m, ےACB = 30⁰&ےADB = 45⁰

AB / AC = tan 30⁰= 1 / √3

So, AC = 100√3 m

AB / AD = tan 45⁰= 1

So, AD = AB = 100 m

So, CD = AC + AD

= (100√3 + 100)m.

Find out more solved and practice questions of Quantitative aptitude and reasoning, click SBI PO & Clerk Exam for details.

There are few questions you can try yourself.

Q1. 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 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

173 m
200 m
273 m
300 m

Ans C

Q2. The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

Ans C
Q3. The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

30 degree
45 degree
60 degree
90 degree

Ans A
Q4. From a point C on a level ground, the angle of elevation of the top of a tower is 30 degree. If the tower is 100 meter high, find the distance from point C to the foot of the tower.

170 m
172 m
173 m
167 m

Ans C
Q5. A man is watching form the top of the tower a boat speeding away from the tower. The boat makes the angle of depression of 45 degree with the man’s eye when at a distance of 60 metres from the tower. After 5 seconds the angle of depression becomes 30 degree. What is the approximate speed of the boat, assuming that it is running in still water ?

22 km/Hr
28 Km/Hr
36 Km/Hr
32 Km/Hr

Ans D

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