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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 \(30^o\) 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 \(60^o\) to the ground. What should be the length of the slide in each case?
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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 \(30^o\) 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 \(60^o\) to the ground. What should be the length of the slide in each case?

Answer

As per contractor’s plan,
Answer for 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^o 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^o to the ground. What should be the length of the slide in each case?
Answer for 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^o 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^o to the ground. What should be the length of the slide in each case?
Let, \(ABC\) is the slide inclined at \(30^o\) with length \(AC \)and \(PQR \)is the slide inclined at \(60^o\) with length \(PR\).
To Find: \(AC \)and \(PR\)
In right \(ΔABC\),
\(\sin 30^o = \frac{AB}{AC}\)
\(\implies \frac{1}{2} = \frac{1.5}{AC}\)
\(\implies AC = 3\)
Also,in right \(ΔPQR\),
\(sin 60^o = \frac{PQ}{PR}\)
\(\implies \frac{\sqrt{3}}{2}\) \(= \frac{3}{PR}\)
\(\implies PR = 2\)\(\sqrt{3}\)
Hence, length of the slide for below \(5 = 3 \ m\) and
Length of the slide for elders children \(= 2\)\(\sqrt{3} \ m\) 
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