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

In $$∆ \ BDE$$

$$\frac{DE}{BD} \ = \ cosec 30º \ => \ \frac{DE}{1.5} \ = \ 2$$

=> $$DE \ = \ 2 × 1.5 \ = \ 3$$

And in $$∆ \ ABC$$

$$\frac{AC}{AB} \ = \ cosec 60º \ => \ \frac{AC}{3} \ = \ \frac{2}{ \sqrt{3}}$$

$$AC \ = \ \frac{2}{ \sqrt{3}} × 3 \ = \ 2\sqrt{3}$$

$$\therefore$$ Length of slides are $$3$$ m and $$2\sqrt{3}$$ m