Question

A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m and inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide (in m)?

• A. 3$\sqrt{3}$
• B. 5
• C. 4$\sqrt{3}$
• D. 6

Answer 1

The correct option is C

4$\sqrt{3}$

The above figure represents the given situation.
In the given right-angled triangle,
$sin\left(\angle ACB\right)=\frac{AB}{AC}\Rightarrow sin{60}^{\circ }=\frac{6}{AC}\Rightarrow AC=\frac{6}{\frac{\sqrt{3}}{2}}=\frac{12}{\sqrt{3}}=4\sqrt{3}m\therefore \text{length of slide}=4\sqrt{3}m$