Height and Distance- Aptitude Questions and Answers

View in English View in Hindi

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

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 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

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

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

Height and Distance

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

Indian History

Who among the following social reformers had founded the Ramakrishna Mission ?

Physics

Who received the first Nobel Prize in physics?

Which among the following is the SI unit of Force?

Atmospheric pressure at sea level equals ?

General Knowledge of India

Which of the following dance forms was introduced by the great Vaishnava saint and reformer Mahapurusha Sankaradeva ?

Which of the following is the only classical dance of india having links with Muslim culture and represents a unique synthesis of Hindu and Muslim genius in art ?

Time and Distance

Starting from the same point at the same time, Ruhan and Yuvan had to reach the same destination. While Ruhan drove at 45 km/hr, Yuvan was slower by 5 km/hr. If Yuvan arrived at the destination an hour after Ruhan did, the distance covered by each, in Kilometres, was ?

Simple Interest

A sum of money was invested at a certain rate of simple interest for 4 years. Had the sum been invested at a rate 3% higher than the actual rate, the interest earned would have been 720 Rs more. Find the sum initially invested?

Ratio and Proportion

A bag contains red, blue and black balls. The ratio of red to blue balls is 3 : 5. The ratio of black to red balls is 3 : 4. What is the ratio of blue to black balls?

Profit and Loss

Selling a pack of incense sticks for 136 Rs resulted in a loss of 15%. To make a profit of 10%, the selling price should be ?

Percentage

23% of a bucket full of diluted milk was water. If the quantity of pure milk in the bucket was 15.4 liter, then the capacity of the bucket was ?

Average

The average of the marks obtained by three girls in a test was twice the average of the marks obtained by eight boys in that test. If the total marks obtained by all these examinees was 168, find the average marks each of the girls obtained ?

Pipes and Cistern

44 pipes can fill a large water tank in 27 hours. How many hours it take for 66 pipes to fill four such tanks ?

HCF and LCM

A natural number, when divided by 3, 4, 5, 6, and 7 respectively, leaves corresponding remainder of 2, 3, 4, 5 and 6. What is the smallest of all such numbers fulfilling the above condition ?

Coding-Decoding

If in a certain code language, PRINT is written as 34825 and TRUE is written as 5479. Then, how will TENURE be written in that language?

Order Sequence

Arrange the given words from smallest to biggest-
1.Jug
2.Mug
3.Bucket
4.Drum
5.Cup

Statement and Conclusion

Statements
All socks are shoes
Some shoes are black

Conclusions
I. Some shoes are socks.
II. No scoks is black