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?

Answer 1

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.