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?

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&deg; 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&deg; to the ground. What should be the length of the slide in each case?

cdquestions Admin · Accepted Answer

It can be observed that AC and PR are the slides for younger and elder children respectively. In  $\triangle ABC$ , $\frac{AB}{ AC} = sin 30°$ $\frac{1.5}{ AC} = \frac{1}2$ $AC = 3m$ In  $\triangle PQR,$ $\frac{PQ}{PR} = sin60°$ $\frac{3}{ PR} = \frac{\sqrt 3}2$ $PR = \frac{6}{\sqrt3}$ $PR = 2\sqrt3 m$ Therefore, the lengths of these slides are  $3 \,m$  and  $2\sqrt3 \,m$ .

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