Aptitude - Height and Distance - Discussion
Discussion Forum : Height and Distance - General Questions (Q.No. 6)
6.
The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:
Answer: Option
Explanation:
Let AB be the tree and AC be its shadow.
Let 
ACB = 
.
| Then, | AC | = | 3  cot = 3 |
| AB |
= 30°.
Discussion:
62 comments Page 5 of 7.
Sandeep sai kumar said:
7 years ago
We consider;
ab=x then,
ca=√3x,
So tanθ=opposite/adjacent.
Tanθ=ab/ac.
Tanθ=x/√3x,
Tanθ=1/√3,
θ=tanθ 1(1/√3),
θ=tan (√3),
θ=30°.
ab=x then,
ca=√3x,
So tanθ=opposite/adjacent.
Tanθ=ab/ac.
Tanθ=x/√3x,
Tanθ=1/√3,
θ=tanθ 1(1/√3),
θ=tan (√3),
θ=30°.
Prashanth said:
7 years ago
This can be tan 60 also right, because the value of tan 60 is √3.
Jeslin said:
7 years ago
Let tree AB=x.
Shadow AC= √3 times height of the tree.
so, AC= √3x.
Here, the opposite and adjacent sides are involved so, we are using tan.
Tan theta = opp/adj =AB/AC =x/√3x =1/√3.
Theta = tan inverseof( 1/√3).
Theta=30°.
(we know that tan 30° =1/√3).
Hope it helps.
Shadow AC= √3 times height of the tree.
so, AC= √3x.
Here, the opposite and adjacent sides are involved so, we are using tan.
Tan theta = opp/adj =AB/AC =x/√3x =1/√3.
Theta = tan inverseof( 1/√3).
Theta=30°.
(we know that tan 30° =1/√3).
Hope it helps.
Pranit Raj said:
6 years ago
Can also the answer be 60° If we consider tan.
Sai Aswin said:
6 years ago
SHORT CUT:
Shadow=√3(height of the tree).
(Shadow/height of tree)= √3,
So, cotθ = √3=30°.
Shadow=√3(height of the tree).
(Shadow/height of tree)= √3,
So, cotθ = √3=30°.
Aravind said:
6 years ago
AB/AC=1/√3.
TANθ=30θ.
TANθ=30θ.
(1)
Nisha said:
6 years ago
Thanks @Balaji.
Vijay Kumar said:
6 years ago
@All.
tanθ=AB/AC = x/√3x.
tanθ=1/√3.
In the important formula table, they were given that the value of tan30 = 1/√3.
Hence here the value of θ becomes 30.
tanθ=AB/AC = x/√3x.
tanθ=1/√3.
In the important formula table, they were given that the value of tan30 = 1/√3.
Hence here the value of θ becomes 30.
Aditya said:
6 years ago
I think answer would be 60° because here angle of elevation of the Sun is asked.
As angle of elevation of the sun increases the length of shadow Decreases and vice versa.
As angle of elevation of the sun increases the length of shadow Decreases and vice versa.
Ravi said:
5 years ago
Here we solve the problem by using the angle of depression. Let β the angle of depression made by the sun on the tree.
Then angle β is equal to the angle of BCA.
Given the length of shadow is √3 times the height of tree i.e., AC=√3AB.
tanβ = AB/AC = AB/√3AB = 1/√3
tanβ = tan30° =>β = 30°.
Then angle β is equal to the angle of BCA.
Given the length of shadow is √3 times the height of tree i.e., AC=√3AB.
tanβ = AB/AC = AB/√3AB = 1/√3
tanβ = tan30° =>β = 30°.
(3)
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