A 18 m long ladder (whose foot is on the ground) leans against a wall making…

20202020

A 18 m long ladder (whose foot is on the ground) leans against a wall making an angle of 30° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground?

  1. A.

    9√3

  2. B.

    (9√3)/2

  3. C.

    18

  4. D.

    9√2

Attempted by 43 students.

Show answer & explanation

Correct answer: A

Given:
Length of ladder = 18 m
The ladder makes an angle of 30° with the wall.
We need to find the height where the ladder touches the wall.
In the right triangle formed:
Hypotenuse = 18 m
Angle with wall = 30°
Required height is adjacent to the angle.
Using:
cos 30° = Height/18
√3/2 = Height/18
Height = 18 × √3/2
= 9√3 m

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