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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, where as for the elder children, she wants to have a steep side at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Solution
It can be observed that AC and PR are the slides for younger and elder children respectively.
In ΔABC,
`("AB")/("AC")` = sin 30°
`1.5/("AC") = 1/2`
AC = 3 m
In ΔPQR,
`"PQ"/"PR"` = sin 60°
`3/("PR") = sqrt3/2`
`"PR" = 6/sqrt3`
= `2sqrt3 m`
Therefore, the lengths of these slides are 3 m and `2sqrt3` m.
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