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A ladder $18 m$ long makes an angle of $60 °$ with a wall. The height of the point where the ladder reaches the wall is:

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9 m

93 m

183 m

18 m

answer is D.

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Detailed Solution

Given,
Length of a ladder is

18 m

.
Angle with the wall is

60 °

.
Let x be the height of the point on the wall where the 18 m long ladder reaches while making an angle of

60 °

with the wall.
Question Image

Finding the height of point on the wall,

cos 60 ° = Height of point on the wall Length of the ladder

⇒ cos 60 ° = x 18 ⇒ x = 18 × cos 60 ° ⇒ x = 18 × 12 ∵ cos 60 ° = 12 ⇒ x = 9 m

Therefore, the required height is 9m.
Therefore, option 4 is correct.

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