Height and Distance- Aptitude Questions and Answers

View in English View in Hindi

A pole of height h = 60 ft has a shadow of length l= 60 ft at a particular instant of time. Find the angle of elevation (in degrees) of the sun at this point of time.

A)
30

B)
45

C)
60

D)
40


Correct Answer :

45


Explanation :

let, hight of the pole = BC and length of shadow is = AB
tan A = Perpendicular/Base = BC / AB = h / l = 60 / 60 = 1
tan A = 1 for A =45o.
Hence the angle of elevation of the sun at this point of time is 45o

Post comment
Cancel
Thanks for your comment.!
Write a comment(Click here) ...
View in English View in Hindi

A boy is flying a kite. The string of the kite makes an angle of 60o with the ground. If the height of the kite is 32 m, find the length (in meters) of the string.

A)
64

B)
32/√3

C)
32√3

D)
64/√3


Correct Answer :

64/√3


Explanation :

Sin q = Perpendicular/Hypotenuse
Sin 60o = 32/ L
L=32/ √3/2

Hence, the length (in meters) of the string L= 64/√3

A person standing on bank of the river observes that the angle subtended by a tree on the opposite bank is 60° and when he retires 40m from the bank, he finds the angle of elevation as 30°. Then the breadth of the river is

A)
40m

B)
20m

C)
22m

D)
35m


Correct Answer :

20m


Explanation :


Let the height of the tree is BC and breadth of the river is AB.
there A was the initial position and D is the final potion of the man

tan 60 =h/x
√3 =h/x
h=x√3 -----------eq(1)

tan 30 = h/ 40+x
1/√3 = h/ 40+x
h=(40+x)/√3

using eq(1)
x√3=(40+x)/√3
3x = 40+x
2x = 40
x = 20

Two men on one sides of a building of height 25 m notice the angle of elevation of the top of the building to be 45o and 60o respectively. Find the distance (in meters) between the two men.

A)
32(1+ (1/√3))

B)
15/√3

C)
25(1-(1/√3))

D)
25√3


Correct Answer :

25(1-(1/√3))


Explanation :


Let In the figure, A and B represent the two men and CD the tall building.
tan A = tan 45= h / AC
tan B = tan 60 = h / BC.
Now the distance between the men is AB
= x = AC − BC = (h / tan 45) − (h / tan 60)
= h((1/ tan 45) − (1/ tan 60 ) )
= 25(1 − (1/ tan 60 ) )
= 25(1 − (1/√3 ) )

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60º and 45º respectively. What is the height of the lower plane from the ground?

A)
100√3 m

B)
100/√3 m

C)
50/√3 m

D)
150(√3 +1) m


Correct Answer :

100√3 m


Explanation :

Let the height of the lower plane from the ground be h m and PA = x

Now, in BAP,
tan45° = AB/AP
1 = h/x
h = x ....eq(i)

Now In APC
tan60° = AC/AP = 300/x
x = 300/√3 ....eq(ii)

From Eqs. (i) and (ii), we get
h = x = 300/√3
= 300*√3 /√3*√3
= 300*√3 /3
= 100√3 m

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30º and 45º respectively. What is the height of the tree?

A)
30√3 m

B)
90-30√3 m

C)
90+30√3 m

D)
60+30√3 m


Correct Answer :

90-30√3 m


Explanation :

Let AB and CD be the building and tree respectively.
Now, in ABD
tan45° = AB/BD
1 = 90/BD
BD = 90 m ...eq(i)

Again, in AEC
tan30° = AE/EC
1/√3 = AE/90
AE = 90/√3 = 30√3 m

Hence, Height of tree = CD = BE = AB-AE = 90-30√3 m

The difference in the length of the shadow of a 10 m high pole when the angles of elevation of the sun are 30° and 60° is

A)
20√3 / 3 m

B)
10√3 m

C)
10√3 / 3 m

D)
10 m


Correct Answer :

20√3 / 3 m


Explanation :


Let AB be the pole and BD, BC is its shadows when the angle of elevation of the sun is 30°, 60° respectively.

in ACB
tan 60° = √3 = AB/BC = 10/BC
BC = 10/√3 = 10√3 / 3

in ADB
tan 30° = 1/√3 = AB/BD = 10/ BC + CD
BC + CD = 10√3
CD = 10√3 - 10√3/3 =(30√3 - 10√3) / 3 = 20√3 / 3

The difference between the length of the shadow, CD = 20√3 / 3

Latest Updates

Indian Geography

What is the approximate distance between earth and the moon?

Indian History

In which year was the battle of ‘Koregaon Bhima’ fought?

The approach that is very useful in organizing the content in history is.

General Knowledge of India

NITI Aayog stands for _____.

General Knowledge of MP

India’s first Ramayan art museum was established at?

Errors Identification

Read the sentence carefully and choose the option that has an error in it:
The management’s trusted employee was suspected of stealing large sum of money.

Read the sentence carefully and choose the option that has an error in it:
The teacher asked the child to repeat again because he spoke feebly.

Fill in the blank

Fill in the blank with the most appropriate preposition in the given sentence.
Let’s sit _________ the shade of this beautiful tree.

Choose the most appropriate determiner for the given sentence.
________of what he said was very sensible.

Substitution

Choose the option that substitutes the given phrase appropriately.
A work of art made by carving

Correct sentence

Choose the option that best transforms the sentence into its Indirect form:
‘What country do you come from?’ said the police officer.

Alternative Phrase

Choose the option that best explains the highlighted expression:
All human beings have feet of clay.

Fill in the blank

Choose an appropriate modal for the given sentence:
My doctor said that I_____ stop smoking as one of my lungs got infected.

Choose the appropriate prepositions for the given sentence:
My parents have been married ________ forty-nine years, but you can still see the love ________ their eyes.

Choose the appropriate conjunction for the given sentence:
______ it rains, the college will declare the holiday.

Antonyms

Choose the appropriate antonym for the highlighted word in the given sentence.
The family protracted their visit by several days.

Tenses

Choose the appropriate tenses to fill in the blanks in the given sentence:
Please _________ a noise. Ritu __________ to sleep.

Synonyms

Choose the appropriate synonym for the highlighted word in the given sentence.
Does he really expect us to believe such a flimsy excuse?

Latest Job Notifications

Jobs in Bihar

बिहार तकनीकी सेवा आयोग / Bihar Technical Service Commission (BTSC) - 12771 पद - 01/09/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान उच्च न्यायालय / Rajasthan High Court - 2756 पद - 22/09/2022 अंतिम तिथि

Jobs in Uttar Pradesh

उत्तर प्रदेश पावर कॉर्पोरेशन लिमिटेड / Uttar Pradesh Power Corporation Limited - 1033 पद - 12/09/2022 अंतिम तिथि

Jobs in Tamil Nadu

तमिलनाडु चिकित्सा सेवा भर्ती बोर्ड / Tamil Nadu Medical Services Recruitment Board (MRB) - 889 पद - 30/08/2022 अंतिम तिथि

Jobs in Andhra Pradesh

आंध्र प्रदेश स्वास्थ्य, चिकित्सा और परिवार कल्याण विभाग / Andhra Pradesh Health, Medical and Family Welfare Department - 1681 पद - 22/08/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 4300 पद - 30/08/2022 अंतिम तिथि - CPO Recruitment

Banking Jobs

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 6432 पद - 22/08/2022 अंतिम तिथि

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 7855 पद - 29/07/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 1411 पद - 29/07/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान अधीनस्थ और मंत्रिस्तरीय सेवा चयन बोर्ड Rajasthan Subordinate and Ministerial Services Selection Board (RSMSSB) - 5546 पद - 22-Jul-2022 अंतिम तिथि