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The angle of elevation of a ladder leaning against a wall is $60 °$ the foot of the ladder is 12.4 $m$ away from the wall. The length of the ladder is

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14.8 m

6.2 m

12.4 m

24.8 m

answer is D.

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Detailed Solution

Given that the angle of elevation of a ladder leaning against a wall is

60 °

the foot of the ladder is 12.4

m

away from the wall.
Let ‘h’ be the length of ladder.
We draw the diagram showing the situation.
Question Image

We know,

cosθ = \frac{Base}{Hypotenuse}

\cos 60 ° = \frac{1}{2}

The length of ladder will be,

\cos 60 ° = \frac{12.4}{h}

Therefore,

h = 12.4 cos 60 ° ⇒ h = 12 ⋅ 4 12 ⇒ h = 24.8 m

Therefore, the required height is 24.8cm.
Thus, option 4 is correct.

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