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# A ladder with 13 meters of length leans on the wall. If the distance

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Intern
Joined: 18 Apr 2013
Posts: 34
A ladder with 13 meters of length leans on the wall. If the distance  [#permalink]

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06 Jul 2017, 08:13
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Difficulty:

45% (medium)

Question Stats:

56% (01:25) correct 44% (01:36) wrong based on 68 sessions

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A ladder with 13 meters of length leans on the wall. If the distance between the bottom of the ladder and the wall is 5 meters, what is the angle between the ground and the ladder?
A) 0 to 15 degrees
B) 15 to 30 degrees
C) 30 to 45 degrees
D) 45 to 60 degrees
E) 60 to 90 degrees
Intern
Joined: 06 Jan 2016
Posts: 27
Re: A ladder with 13 meters of length leans on the wall. If the distance  [#permalink]

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06 Jul 2017, 09:11
My approach was based on the known angle and sides relationships for the GMAT.

Precisely the 1:1:\sqrt{2} and the 1:\sqrt{3}:2

First we have to find the value for the unknown side which yields 12, and we already can see that the hypotenuse and the calculated leg values are quite close. Therefore we only have left the options D) and E).

Is the angle bigger than 60º? with the answer to this question we will know the right answer. So we need to find how the ratios between known angles and sides work as you can see in the attachment the bigger the ratio the bigger the angle. So if the relationship 13/5 is bigger than the relationship 2/1 then the angle will be bigger than 60º and, in fact, it is. Thus the correct answer is E)
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File comment: Graphical solution

photo_2017-07-06_18-05-28.jpg [ 86.34 KiB | Viewed 728 times ]

Intern
Joined: 09 Jan 2017
Posts: 2
Re: A ladder with 13 meters of length leans on the wall. If the distance  [#permalink]

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07 Jul 2017, 13:13
As we already know that cos(60) is 0.5 and value decreases as we go towards 90 degrees in cos function.
In the given problem, base is 5 and hypotenuse is 13 which suggests cos(angle) = 5/13 which is less than 0.5
So, we can fairly think that the angle would be more than 60 degrees.
Hence the answer is E - 60 to 90 degrees.
Re: A ladder with 13 meters of length leans on the wall. If the distance   [#permalink] 07 Jul 2017, 13:13
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