The distance between the tops of two trees $20 m$ and $28 m$ high is $17 m .$ The horizontal distance between the trees is

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Solution

Let $A B$ and $C D$ be two trees such that $A B = 20 m, C D = 28 m$ and $B D = 17 m$

Draw $B E ⊥ C D$ .
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Then, $E D = C D - A B = 28 - 20 = 8 m$ .

In $△ B E D$ , applying Pythagoras Theorem

$B D^{2} = B E^{2} + D E^{2}$
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$\Rightarrow B E^{2} = B D^{2} - D E^{2}$

$\Rightarrow B E^{2} = 17^{2} - 8^{2} = 289 - 64 = 225$

$\Rightarrow B E = \sqrt{225} = 15 m$

$\Rightarrow A C = B E = 15 m$
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