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?
Length of slide for children below 5 years (height 1.5 m, angle 30°)
Length of slide for children below 5 years = 3 m
Length of slide for elder children (height 3 m, angle 60°)
Length of slide for elder children = 2 m (or approximately 3.46 m)
Explanation
This question involves finding the hypotenuse (length of slide) when the opposite side (height) and angle are given. The context shows in Example 2 that when we need to find the hypotenuse given the opposite side and angle, we use the sine ratio: sin θ = opposite/hypotenuse. This same approach applies to both slides.