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 $1.5m$, and is inclined at an angle of ${30}^o$ 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 ${60}^o$ to the ground. What should be the length of the slide in each case?

Answer 1

$\left(i\right)AB=1.5m,AC=l_{1}m,\angle ABC={30}^0$

In $\perp \Delta ABC,\angle B={90}^0$

$\frac{AB}{AC}=sin{30}^0$

$\frac{1.5}{l_1}=\frac{1}{2}$

$\therefore l_1=2\times .5=3m$

$\therefore$ length of slide of younger children $=3m$

(ii) $PQ=3m,Op=12m,\angle POQ={60}^0$

In $\perp \Delta PQR,\angle Q={90}^0$

$\frac{PQ}{OP}=sin{60}^0$

$\frac{3}{l_2}=\frac{\sqrt{3}}{2}$

$l_2=\frac{3\times 2}{\sqrt{3}}$

$\therefore l_2=2\sqrt{3}m$

$\therefore$ length of slide of elder children = $2\sqrt{3}m$