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A ladder, leaning against a wall, makes an angle of $60 °$ with the horizontal. If the foot of the ladder is $2.5 m$ away from the wall, find the length of the ladder.

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3

1

2

5

answer is A.

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Detailed Solution

Given that, the ladder, leaning against the wall makes an angle of

60 °

with the horizontal and the distance between the foot of the ladder from the base of wall is 2.5 m.
Draw the diagram depicting the situation.
Question Image

Calculating the length of the ladder using the trigonometric ratio

cos θ = Base Hypotenuse

cos 60 ° = 2.5 length ⇒ length = 2.5 cos 60 ° ⇒ length = 2.5 0.5 ⇒ length = 5

The length of the ladder leaning on a wall which makes

60 °

angle with the horizontal and is 2.5 m away from the base of the wall is 5 m.
Hence the correct option is 1.

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