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Applications of Trigonometry
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17/06/2021 10:53 am
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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° 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° to the ground. What should be the length of the slide in each case?
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17/06/2021 10:56 am
As per contractor’s plan,
Let, ABC is the slide inclined at 30° with length AC and PQR is the slide inclined at
60° with length PR.
AC and PR
In right ΔABC,
sin 30° = AB/AC
1/2 = 1.5/AC
AC = 3
In right ΔPQR,
sin 60° = PQ/PR
⇒ √3/2 = 3/PR
⇒ PR = 2√3
Hence, length of the slide for below 5 = 3 m
Length of the slide for elders children = 2√3 m