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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 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 to the ground. What should be the length of the slide in each case?

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Solution

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 with length AC and PQR is the slide inclined at 60 with length PR.
As per the question,
In right ΔABC,
sin30=ABAC
12=1.5AC
AC=3m

In right ΔPQR,
sin60=PQPR
32=3PR
PR=23 m
Hence, length of the slides are 3 m and 23 m respectively.

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