Question:
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 degree 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 degree to the ground. What should be the length of the slide in each case?
Answer:
In the first figure and from triangle BCD
sin30 = BC/BD
=>1/2 = 1.5/BD
=> BD = 1.5*2
=> BD = 3
So lenght of slide for child below 5 years = 3 m
Again in the second figure and from triangle BCD
sin60 = BC/BD
=>√3/2 = 3/BD
=> BD = (3*2)/√3
=> BD = (√3*√3*2)/√3
=> BD = 2√3
So lenght of slide for child greater than 5 years = 2√3 m
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