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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 1.5m, 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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Solution

Step 1: Finding the length of the slide for younger children.

Let ABC be the slide for the children below the age of 5 years and PQR be the slide for the elder children.

In ABC,B is the right angle and C=30°.

We know that, sinθ=PerpendicularHypotenuse

sin30o=ABAC12=1.5ACAC=1.5×2AC=3m

Step 2- Finding the length of the slide for elder children

Sinθ=PerpendicularHypotenuseSin60o=PQPR32=3PRPR=63PR=63×33PR=63×3PR=23PR=2×1.73PR=3.46m

Hence, the length of slide for the children below the age of 5 is 3m, and for the elder children is 3.46m.


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