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
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:
- 3 m
- 6 m
- 2 m
- 8 m
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
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
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
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