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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 shows 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 3 m, and inclined at an angle of 60° to the ground. What should be length of the slide In each case?

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Case I When contractor installs slide for children below the age of 5 years then its height AB = 1.5 m and ∠ACB = 30°

Let length of slide AC = x m

From right angled ∆ABC

sin 30° = AB/AC

⇒ 1/2 = 1.5/x

⇒ x = 1.5 × 2

∴ AC = 3 m

Case II. When contractor installs slide for children above  the age of 5 years then its height PQ = 3 m and ∠PRQ = 60°

Let length of slide PR = y m

From right angled ∆PQR

Hence, length of slide for children below the age of 5 years = 3 m and above the age of 5 years = 2√3 m.

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