Question

A contractor plans 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 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?

• A. $5m$ is the length of the slide made for children below the age of 5 years and $3m$ is the length of the slide made for elder children.
• B. $3m$ is the length of the slide made for children below the age of 5 years and $2\sqrt{3}m$ is the length of the slide made for elder children.
• C. $7m$ is the length of the slide made for children below the age of 5 years and $5m$ is the length of the slide made for elder children.
• D. $2m$ is the length of the slide made for children below the age of 5 years and $7\sqrt{2}m$ is the length of the slide made for elder children.

Answer 1

The correct option is B $3m$ is the length of the slide made for children below the age of 5 years and $2\sqrt{3}m$ is the length of the slide made for elder children.

In figure, $l_1$ is the length of the slide made for children below the age of 5 years and $l_2$ is the length of the slide made for elder children.
In figure, $AB=1.5m,AC=l_{1}m$ and $\angle ACB={30}^o;PQ=3m;OP=l_{2}m$ and $\angle POQ={60}^o$
$\frac{AB}{AC}=\sin {30}^o$ and $\frac{PQ}{OP}=\sin {60}^o$
$\Rightarrow$ $\frac{1.5}{l_1}=\frac{1}{2}$ and $\frac{3}{l_2}=\frac{\sqrt{3}}{2}$
$\Rightarrow$ $l_1=2\times 1.5m$ and $l_2=\frac{3\times 2}{\sqrt{3}}m$
$\Rightarrow$ $l_1=3m$ and $l_2=2\sqrt{3}m$