Aptitude - Height and Distance - Discussion

Discussion :: Height and Distance - General Questions (Q.No.3)


The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

[A]. 2.3 m
[B]. 4.6 m
[C]. 7.8 m
[D]. 9.2 m

Answer: Option D


Let AB be the wall and BC be the ladder.

Then, ACB = 60° and AC = 4.6 m.

AC = cos 60° = 1
BC 2

BC = 2 x AC
= (2 x 4.6) m
= 9.2 m.

Shyam said: (Mar 26, 2011)  
Why the above two problem we taking "tan", but for this problem we took "cos". Anyone explain ?

Ashish said: (Jun 17, 2011)  
Can we do it taking tan?

Nikita said: (Aug 10, 2011)  
Shyam and Asish,

Absolutely we can take tan.
but if we take tan we will get AB.
Then we have to take sin to find length of the ladder, i.e BC.

It 'll take more time..so only we take cos in this problem.

Shine said: (Sep 27, 2011)  
Nikita great Ans thanks

Shiyamala Maths said: (Sep 9, 2012)  
sin=Opposite side/hypotenuse

cos=adjacent side/hypotenuse



We know adjacent side that is only we are using cos


=AC/AB = 1/2 {cross multiplication)




Cynthia said: (Dec 21, 2013)  
Why can't we take in this way:

Tan 60 = AB/4.6.

1.73 = AB/4.6.
AB = 7.958.

Anand said: (Jun 20, 2014)  
Short cut of sin, cos, tan are.

sin = old/harry (opposite/hypotenuse).
cos = and/his (adjacent/hypotenuse).
tan = old/aunty (opposite/adjacent).

(note:check first letter).

Vikram said: (Sep 17, 2014)  
Why we are using cos here?

Fgrg said: (Oct 11, 2014)  
Can't we do this with the 30, 60, 90 triangle method?

Anant said: (Jul 25, 2015)  
tan60 = x/4.6.

x = tan60*4.6.
x = 1.732*4.6.

Therefore, x = 7.8.

Lucifer123 said: (Nov 5, 2015)  

No wonder girls are dumb.

We want "BC" (the length of the ladder) not "AC" (height of the wall).

Manjunath said: (Jan 5, 2016)  
They are asking 4.6 m away from the wall. But here its get attach with the wall. How come?

Sreeja said: (Apr 20, 2016)  
How can we remember here we should use "Tan" and there we should use "Cos"?

Rahul Rami said: (Jun 30, 2016)  
Its very simple @Sreeja.

If we have perpendicular (AB) and say to find hypotenuse (BC) then we use sin Angle.

If we have perpendicular (AB) and say to find Base (AC) then we use tan Angle.

If we have Base (AC) and say to find Hypotenuse (BC) then we use Cos angle.

Note : AB, AC, BC are taken from the solution of this question,

In above example, we have a base (AC) and say to the fine length of ladder means find hypotenuse (BC).

So we can use Cos Angle in this situation.

Cateyes said: (Jul 10, 2016)  
Also according to the position of angle. We decide which one is opposite side and which one is adjacent. So remember the formula for each Sin, Cos, and Tan and solve the problem easily.

Praveen Kumar said: (Jan 14, 2017)  
Great answer Thanks @Rahul Rami.

Rajan said: (Jan 15, 2017)  
Why can't we use sec instead of cos?

Prasanna Kumar said: (Jun 29, 2017)  
Why was the down angle is 60 degrees, angle of elevation means top angle should be top angle should be zero?

Jit said: (Jul 12, 2017)  
If we take,


Why can't we solve in this way?

Sahil said: (Sep 18, 2017)  
We can do it using tan also.

Viraj said: (Dec 15, 2017)  
How to find √3?

Priya said: (Mar 31, 2018)  
Because of cos = adjacent/hypotenuse if we take tan it becomes AB/AC we need a length of the ladder ie BC so we take cos, ie AC/BC.

Prasad Chachadi said: (Jul 2, 2018)  
Here, the elevation with respect to the wall but in the solution, it is taken with respect to the land!

Please correct me, if I am wrong.

Gaurav said: (Jul 13, 2018)  

How these combinations of base and perpendicular, hypotenuse and perpendicular, hypotenuse and base and so on are formed?

Just tell where is the rule that cos will be equal to Base/Perpendicular rather than Base/Hypotenuse?

Puneet Kulkarni said: (Aug 2, 2018)  
We have formula:


Neeraj said: (Dec 7, 2018)  
Why can't we solve this using tan?

Bhavy said: (Feb 1, 2019)  

Sin=perpendicular. Upon hypotenuse and cos, =base upon hypotenuse and tan=perpendicular upon base. And in this question, we need hypotenuse so cos is applied.

Chiru said: (Jul 20, 2019)  

Here, it is mentioned that the ladder is leaning on the wall, AB is the wall and BC is the ladder that's the reason we taken Tan.

Brinda said: (Jul 23, 2019)  

Yes, you are right and when Tan is taken answer is 7.9.

Niezel said: (Aug 7, 2019)  
By using tan you'll end up getting AB which is B the height of the wall but the problem says to find for the length of the ladder then use the value of AB and AC using Pythagorean's theorem c= √(a^2+b^2).

Then BC= √(AB^2 + AC^2) then you"ll get the length of the ladder.

Altamash Bagwan said: (Jan 23, 2020)  
In this question, cos indicate is an adjacent side/hypotenuse side.

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