Question

Question 3
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 ${30}^{\circ }$ to the ground whereas for elder children she wants to have a steep slide at a height of 3 m and inclined at an angle of ${60}^{\circ }$ to the ground. What should be the length of the slide in each case?

Answer 1

There are two slides of height 1.5 m and 3 m.
Let AB be 1.5 m and PQ be 3 m.


ABC is the slide inclined at ${30}^{\circ }$ with length AC and PQR is the slide inclined at ${60}^{\circ }$ with length PR.
As per the question,
In right $\Delta ABC$,
$sin{30}^{\circ }=\frac{AB}{AC}$
$\Rightarrow \frac{1}{2}=\frac{1.5}{AC}$
$\Rightarrow AC=3m$

In right $\Delta PQR$,
$sin{60}^{\circ }=\frac{PQ}{PR}$
$\Rightarrow \frac{\sqrt{3}}{2}=\frac{3}{PR}$
$\Rightarrow PR=2\sqrt{3}$ m
Hence, length of the slides are 3 m and $2\sqrt{3}$ m respectively.