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An electrician has to repair an electric fault on a pole of height $4 m$ . He needs to reach a point $1.3 m$ below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which when inclined at an angle of $60 °$ to the horizontal would enable him to reach the required position?

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4.12 m

5.12 m

3.12 m

6.12 m

answer is A.

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Detailed Solution

Given,
Height of a pole =

4 m

.
A point below the top of the pole to undertake the repair work =

1.3 m

.
Consider the diagram,
Question Image

The length of the ladder using the trigonometric ratio,

sin θ = Perpendicular Hypotenuse

\Rightarrow \sin 60 ° = \frac{4 - 1.3}{length}

\Rightarrow length = \frac{2.7}{\sin 60 °}

\Rightarrow length = \frac{2.7 \times 2}{\sqrt{3}} \{∵ \sin 60 ° = \frac{\sqrt{3}}{2}\}

\Rightarrow length \approx 3.12 m

The length should be approximately 3.12 m to reach the desired height on the pole.
Therefore, option 1 is correct.

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