Question:
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas 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 in each case?
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas 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 in each case?
Updated On: Jan 13, 2026
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Solution and Explanation
It can be observed that AC and PR are the slides for younger and elder children respectively.
In \(\triangle ABC\),
\(\frac{AB}{ AC} = sin 30°\)
\(\frac{1.5}{ AC} = \frac{1}2\)
\(AC = 3m\)
In \(\triangle PQR,\)
\(\frac{PQ}{PR} = sin60°\)
\(\frac{3}{ PR} = \frac{\sqrt 3}2\)
\(PR = \frac{6}{\sqrt3}\)
\(PR = 2\sqrt3 m\)
Therefore, the lengths of these slides are \(3 \,m\) and \(2\sqrt3 \,m\).
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