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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 whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder

3. 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?

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Suppose x m is the length of slides for children below 5 years and the length of slides for elders children be y m.

Given that,
AF = 1.5 m, BC = 3 m, \angle AEF = 30^o and \angle BDC = 60^o

In triangle \DeltaEAF,
\sin \theta = \frac{AF}{EF} = \frac{1.5}{x}
\sin 30^o = \frac{1.5}{x}
The value of x is 3 m.

Similarily in \DeltaCDB,
\sin 60^o = \frac{3}{y}
\frac{\sqrt{3}}{2}= \frac{3}{y}
the value of y is 2\sqrt{3} = 2(1.732) = 3.468

Hence the length of the slide for children below 5 yrs. is 3 m and for the elder children is 3.468 m.

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