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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 1.5m, 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?

Solution:

Younger children
In ΔABC
sin30° = BC/AC
1/2 = 1.5/AC
∴AC = 3m

Elder children
YZ/XZ = √3/2
XZ = 6
√3 = 2√3m