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A contractor plans to install slides for the children to play in a park. for elder children, she wants to have a steep slide at a height of 3m and inclined at an angle of 60° to the ground. What should be the length of the slide?

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$2 \sqrt{2}$ m

$4 \sqrt{2}$ m

$4 \sqrt{3}$ m

$2 \sqrt{3}$ m

answer is C.

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Detailed Solution

Let, PQR is the slide inclined at 60° and the length be PR.

In right ΔPQR,

sin 60° = $\frac{P Q}{P R}$

$\Rightarrow$ $\frac{\sqrt{3}}{2}$ = $\frac{3 m}{P R}$

$\Rightarrow$ PR = $\frac{6 m}{\sqrt{3}}$

$\Rightarrow$ PR = $\frac{6 m}{\sqrt{3}}$ X $\frac{\sqrt{3}}{\sqrt{3}}$

$\Rightarrow$ PR = $2 \sqrt{3}$ m is our answer.

$∴$ The length of the slide = $2 \sqrt{3}$ m.

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