What is the angle of elevation of the sun when the length of shadow of a tree is root 3 times the height of the tree?

Discussion :: Height and Distance - General Questions (Q.No.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:

[A].	30°
[B].	45°
[C].	60°
[D].	90°

Answer: Option A

Explanation:

Let AB be the tree and AC be its shadow.

Let

ACB =

Then,	AC	=	3 cot = 3
AB

= 30°.

Idiotshere said: (Oct 12, 2010)
Help me please!. I'm not getting here why we are saying ACB why don't BCA ? And another is that why AC/AB why don't AB/AC = tan60 ?

Kapil said: (Dec 15, 2010)
Angle ACB = Angle BCA There are different ways to do same question. they are using cot @ =AC/BC but you can also use tan @ = perpendicular/base = AB/AC

Balaji said: (Feb 11, 2011)

Let me explain here, here carefully,

Here in the problem tree is taken as perpendicular i.e. AB and they also informed that the shadow of tree 3 times the tree i.e. 3 AB. Here shadow is nothing but base.

So we have formula that cot thita = cos θ/ sin θ Cot θ= AC/AB

= 3 * AB/AB

Cot θ= 3 Cot θ= Cot 30

θ = 30

Appu said: (Feb 13, 2011)
Thank you Balaji.

Anchal said: (Jun 13, 2011)

We can also solve like this...let AB=x, then AC=3x, Now AB/AC=tanθ

then x/3=tanθ

After crossing x from x..we get

1/3=tanθ

so tan 30=1/3
so θ=30...Ans..

Kanaga said: (Jun 26, 2011)
Hi, I am not getting the question correctly. They have asked about the angle of elevation of sun. Why should we go for angle of elevation of tree?

Baribie said: (Jul 1, 2011)
Can any one explain the question?

Mjp said: (Jul 3, 2011)
The sun forms a angle of depression. So as the sun is very far away it is hard to take the value, so we can take the angle of elevation of a tree which is equal to the angle of depression.

Kanaga said: (Jul 16, 2011)
@Mjp:Thanks!!!

Shro said: (Feb 20, 2012)
Thanks Balaji

Dendup said: (Oct 12, 2012)
may i know how AC/AB is related to cot@??

Maddy said: (Nov 19, 2012)
Since you know that tan @ = P/B that is AB/AC. And the opposite of tan @ is cot@= B/P that is AC/AB. I hope it will help you to understand.

Xmp said: (Oct 30, 2014)
What is the value of AC & AB?

Manu said: (Feb 18, 2015)
Consider the height of the tree is 'x' m. Then the shadow is (3)^1/2. And apply tan or cot based on the relation which you want to find.

Aparna said: (Jul 3, 2015)
Why don't we consider tan 60 here?

Sanjay said: (Sep 22, 2015)
Ya question has some mistake it's not 3. It's 3^1/2.

Lavanya said: (Oct 23, 2015)
Guys they said shadow of the tree is root 3 times of its height that is if we take height as "x" then base is "root 3x". If we do by using Tan then: Tan theta = Height/Base. = x/root 3x. By cancelling we will get 1/root 3. Theta = tan-1(1/root 3). i.e theta = 30 that's it.

Shiyas said: (Nov 30, 2015)
@Lavanaya. How you cancel "x/root 3x" as "x/root3"? I think it is wrong.

Ashish Kaushik said: (Dec 27, 2015)
Its simple let AB = x then ac = root3x. Tan theta = ab/ac = x/root 3x = 1/root3. Then tan theta =1/root3 = 30 degree.

Palash said: (Mar 19, 2016)
I am not getting the question's meaning. They have included two objectives (tree as well as sun) but which one should I take to solve this problem correctly. Please tell me friends.

Sakthi said: (Jun 27, 2016)
They asking only height of the tree. So the given answer is the correct one.

Nitin said: (Aug 6, 2016)
The question says the heights of the tree is 3 times the shadow of the tree but the correct answer comes only when we take root 3 times?

Tharun said: (Aug 14, 2016)
Cot 30 = tan 60.

Kshyama Sagar said: (Aug 24, 2016)
Considering the above Fig. Assume that the angle of elevation made by the Sun in the shadow of tree is < acb= θ and height of tree (AB) is = x (in meter). According to question, shadow of the tree is √3 times the height of the tree. shadow of a tree(CA) will be = √3x. tan θ = AB/AC = x/√3x. tan θ =1/√3. tan θ = tan 1/√3. tan θ = tan30°. θ = 30° (Require answer).

Vinay said: (Dec 11, 2016)
Can anyone explain me taking of angle ACB and why not ABC? Am thinking the eye of the sun for elevation is from b.

Madhav said: (Dec 14, 2016)
Tan60 = 1/3.

Aadil said: (Feb 27, 2017)
Angle = Tan inverse of( Opposite side/ Adjacent side). So, the Final answer is 30 deg. As tan inverse of 1/root3.

Sangeethasendhil. said: (Jul 12, 2017)
Cot θ = root 3. Then θ =30°; I can't understand this step, can anyone this calculation?

Mahendra said: (Jul 22, 2017)
Let height of the shadow = x. Then the shadow of the is root3 times the height of the tree = root3x. Nnow tan θ =x/root3x. x,x gets cancel and 1/3 remains. we know the tan1/3 = 30°.

Mahesh said: (Sep 13, 2017)
Why cot or tan, why don't we take sine or cosine?

Shaik Sajid said: (Nov 12, 2017)
Hey answer is cot 30 degrees but we can also say tan 60 degrees. Because in the options 60 also there.

Sajid said: (Nov 12, 2017)
Why can't we say tan 60?

Sivaji said: (Dec 1, 2017)
How to take a cotθ formula?

Aniket said: (Jan 17, 2018)
We can also take tan instead of cot.

Amul said: (Mar 16, 2018)
How can say that cot 30°? tan 60 is not compatitable at all I think sin60 or cos60 would be right choice.

Kelzhenry said: (Mar 21, 2018)
AB/AC = Tanθ. From the question, AB/√3AB =Tanθ 1/√3 = Tanθ θ = 30°.

Biplab Gorai said: (Apr 19, 2018)
Thanks for the given solution.

Akhila V U said: (May 23, 2018)
Cot θ= AC/AB. Cot θ =(3 * AB)/AB, Cot θ= 3. Therefore : θ = 30.

Swapnali Wadhavne said: (Jun 17, 2018)
Here shadow is √3 times the tree height. Therefore AC=√3AB. NOW tanθ =AB/AC, tanθ =AB/√3AB, tanθ=1/√3, θ=tan^-1((1/√3)), θ=30°.

Dattatray said: (Jun 22, 2018)
Let x be the height of tree and shadow length √3 x, Tanθ= x &div √3 x. θ=tan-1(1 &div √3), θ=30.

Sandeep Sai Kumar said: (Sep 2, 2018)
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°.

Prashanth said: (Sep 14, 2018)
This can be tan 60 also right, because the value of tan 60 is √3.

Jeslin said: (Sep 20, 2018)
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.

Pranit Raj said: (Feb 7, 2019)
Can also the answer be 60° If we consider tan.

Sai Aswin said: (Feb 15, 2019)

SHORT CUT: Shadow=√3(height of the tree). (Shadow/height of tree)= √3,

So, cotθ = √3=30°.

Aravind said: (Apr 9, 2019)
AB/AC=1/√3. TANθ=30θ.

Nisha said: (Jul 28, 2019)
Thanks @Balaji.

Vijay Kumar said: (Sep 3, 2019)
@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.

Aditya said: (Dec 25, 2019)
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.

Ravi said: (Mar 10, 2020)
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°.

Lory said: (Mar 14, 2020)
I can't understand the question yet.

Vaibhav said: (Jul 21, 2020)
Thank you all for explaining.

Shruti Jalkote said: (Aug 30, 2020)
Thanks all.

Aditi said: (Sep 18, 2020)
Here we are taking base AC as a shadow of height then we can solve it like; Given- Shadow of a tree is √3 times the height of the tree. Height = √3AB. 3AB/AC. 3 = AC/AB. tan = 1/cot. tan = Perpendicular/Base so the inverse of tan is cot. Cot = AC/AB (Base/Perpendicular). Cot 3 = 30°.

Aditya said: (Nov 6, 2020)
Why cot is taken here. Why we cannot take tan? Please explain me.

Gurpreet said: (May 12, 2021)
Thanks all.

Vivek Sunny said: (Nov 23, 2021)
@Aditya. We can choose any ratio either tan or cot. But, which relates both adjacent and height.

Nicholas Hatontola said: (Jul 15, 2022)
Why are we considering BC as the length of the shadow instead of AC? Isn't the shadow supposed to be the base? Please explain me.