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, 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?

Answer 1

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 $2\sqrt3 \,m$.