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

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Bunuel
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A ladder with 13 meters of length leans on the wall. If the distance [#permalink] New post   13 Jun 2019, 00:38
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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
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firas92
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Re: A ladder with 13 meters of length leans on the wall. If the distance [#permalink] New post   13 Jun 2019, 01:39
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The ladder forms a 5-12-13 right angled triangle with the wall and the ground.

Since the ladder's length and the distance between the top of the ladder and the ground are almost equal (12 & 13), the angle between the ground and the ladder must be less than and close to 90 degrees

Answer is (E)

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A ladder with 13 meters of length leans on the wall. If the distance [#permalink] New post   Updated on: 13 Jun 2019, 01:53
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Bunuel wrote:
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



The ladder will form a right angled triangle of lengths, 5 meters,12 meters, 13 meters

Applying sine rule.

((a)/sin(A))= (b/(sin B))

13/sin 90= 12 /sin B
Sin B=12/13
B= sin inverse of (12/13)

B=67.37 degrees

IMO the answer is E

Originally posted by Jansaida on 13 Jun 2019, 00:59.
Last edited by Jansaida on 13 Jun 2019, 01:53, edited 1 time in total.
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A ladder with 13 meters of length leans on the wall. If the distance [#permalink] New post   29 Jul 2020, 23:34
firas92 wrote:
The ladder forms a 5-12-13 right angled triangle with the wall and the ground.

Since the ladder's length and the distance between the top of the ladder and the ground are almost equal (12 & 13), the angle between the ground and the ladder must be less than and close to 90 degrees

Answer is (E)

Hit Kudos if this helped!


For an angle of 30 degrees, the ratio of side opposite to 30 degrees angle and the hypotenuse is 1/2.
For an angle of 45 degrees, the ratio of side opposite to 45 degrees angle and the hypotenuse is 1/\sqrt{2}.

As the angle is decreasing, the ratio is increasing.

Now, 5/13 is less than 1/2, means the angle should be less than 30 degrees in a right angle triangle.

Hence, the other angle will lie between 60 and 90.

OA: E

Bunuel chetan2u : Please correct me if my approach is wrong.
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Re: A ladder with 13 meters of length leans on the wall. If the distance [#permalink] New post   05 May 2023, 15:52
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Re: A ladder with 13 meters of length leans on the wall. If the distance [#permalink]
05 May 2023, 15:52
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