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 shows top is at a height of $1.5m$ and is inclined at an angle of ${30}^0$ 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 ${60}^0$ to the ground. What should be length of the slide In each case?

Answer 1

Case I

When contractor installs slide for children below the age of $5$ years then its height $AB=1.5m$ and

$\angle ACB={30}^0$

Let length of slide $AC=x$ m

From right angled $\Delta ABC$

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

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

$x=1.5\times 2$

$\therefore AC=3m$

Case II.

When contractor installs slide for children above the age of $5$ years then its height $PQ=3m$ and $\angle PRQ={60}^0$

Let length of slide $PR=y$ m

From right angled $\Delta PQR$

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

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

$\sqrt{3}y=3\times 2$

$y=\frac{6}{\sqrt{3}}=\frac{\sqrt{3}}{\sqrt{3}}$

$=\frac{6}{3}\sqrt{3}=2\sqrt{3}m$

Hence, length of slide for children below the age of $5$ years = $3m$ and above the age of $5$ years = $2\sqrt{3}m$.