What is the height of building?

@ishan-nohePN • Oct 26, 2024

Oct 26, 2024

1.4K

This is a question from IIT Powai aptitude test. My friend could not find enough time to solve it. Me too took about 2 hours to solve it only to find that it is a 10th grade question. Here is some food for your brain. There is a building in some place which casts its shadow because of sun. After sometime, the sun rises by 30 degrees hence the shadow length decreases by 10 m. The sun may or may not be at the top of building. Can you find the height of building? I am giving the answer in advance because I will not be available to provide it. It is 17.32 m. Now finding the numerical value is easy. Your real job is to post the logic behind it. Rack your brains. All the best

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ISHAN TOPRE

@ishan-nohePN • Jul 26, 2012

No body could attempt it? Is it this tough?

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Prashanth_p@cchi

@prashanth-p-at-cchi-rg0z63 • Aug 8, 2012

#-Link-Snipped-# : Can you please provide the answer for this?

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ISHAN TOPRE

@ishan-nohePN • Aug 10, 2012

The answer is provided. You need to read the initiation post carefully.

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Prashanth_p@cchi

@prashanth-p-at-cchi-rg0z63 • Aug 11, 2012

IssueThe answer is provided. You need to read the initiation post carefully.
Logic?

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Ramani Aswath

@ramani-VR4O43 • Aug 12, 2012

Since the answer is provided, one can work backwards.
It is also given that the sun may or may not be overhead, which implies that being overhead is not banned. Let us consider the sun overhead. The shadow will have zero length. What will be the angle less than 90 for which the shadow will be 10 m? Simple trigonometry tells that when the sun is 60 degrees above horizon the shadow will be 1/sqrt(3) times the height, in this case 10 m. The difference in the shadow length = 10 - 0 = 10 for an angle difference of 30 degrees.
At all other angles the difference is a function of the angle and hence not defined.

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graphite

@graphite-tkk1sC • Aug 12, 2012

Logic behind it is to use the 30-60-90 triangle theorem we which learned in 10 std. Using that we can calculate the height of building.
Am I correct?

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Ramani Aswath

@ramani-VR4O43 • Aug 12, 2012

graphiteLogic behind it is to use the 30-60-90 triangle theorem we which learned in 10 std. Using that we can calculate the height of building.
Am I correct?
Looks like that.
The logic is that the difference in shadow length of 10 m for a change in the angle of elevation of the sun of 30 degrees has a unique solution only for the initial angle of 60 degrees.

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graphite

@graphite-tkk1sC • Aug 12, 2012

Ok Sir #-Link-Snipped-#
i got it. Thank you.

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zaveri

@zaveri-5TD6Sk • Aug 12, 2012

sounds like a trigonometry problem, but don't have the patience to solve it.

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Saandeep Sreerambatla

@saandeep-sreerambatla-hWHU1M • Aug 16, 2012

THe answer is possible only under the assumption that sun is over head. IF we assume that, its a trignometry problem as #-Link-Snipped-# sir solved it.

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anuraadha

@anuraadha-57t1B5 • Aug 17, 2012

Isolved it just now. But saw that it is already solved 😔

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ISHAN TOPRE

@ishan-nohePN • Aug 18, 2012

English-ScaredTHe answer is possible only under the assumption that sun is over head. IF we assume that, its a trignometry problem as #-Link-Snipped-# sir solved it.
Ok, let me give an explanation. Here is the theorem.

For a give selected angle, in a triangle whether right angled triangle or not, the length of side opposite side to the angle remains same until the angle remains unchanged.
So, whether the sun is overhead or not, the length 10 m which is the side opposite to 30 deg angle remains same. Now by suitable assumptions, we say that the sun is overhead the building and calculate the height of building by using Pythagoras rule i.e. Bodhayan Prameya.

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anuraadha

@anuraadha-57t1B5 • Aug 19, 2012

IssueOk, let me give an explanation. Here is the theorem.

So, whether the sun is overhead or not, the length 10 m which is the side opposite to 30 deg angle remains same. Now by suitable assumptions, we say that the sun is overhead the building and calculate the height of building by using Pythagoras rule i.e. Bodhayan Prameya.
What are the assumptions? And when the sun is right on top of the building , it won't cast its shadow. I solved the problem not assuming the sun overhead. As they have given in the beginning that the building casts a shadow.

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Ramani Aswath

@ramani-VR4O43 • Aug 20, 2012

IssueFor a give selected angle, in a triangle whether right angled triangle or not, the length of side opposite side to the angle remains same until the angle remains unchanged.
I do not understand this. The minimum length of the side opposite a 30 degree angle will be half the hypotenuse in a right triangle. If it is not a right triangle, the length can be anything up to infinity, depending on the other two angles.

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Prashanth_p@cchi

@prashanth-p-at-cchi-rg0z63 • Aug 22, 2012

IssueOk, let me give an explanation. Here is the theorem.
For a give selected angle, in a
triangle whether right angled
triangle or not, the length of side
opposite side to the angle remains
same until the angle remains
unchanged.
Oh! I dnt get ths. Shud dat angle in italics be changed to 'angle and the length of other two sides'??? I thnk dat shud make some meaning.

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rahul tripathi

@rahul-tripathi-ZIdZ9S • Aug 25, 2012

15

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