# Two poles are standing on a horizantal ground are of heights $5\:m\:\:and\:\:10\:m$ respectively . The line joining their tops makes an angle of $15^{0}$ with the ground . Then the distance ( in m ) between the poles, is :Option 1)$5(2+\sqrt{3})$Option 2)$5(\sqrt{3}+1)$Option 3)$\frac{5}{2}(2+\sqrt{3})$Option 4)$10(\sqrt{3}-1)$

$\\\tan\:15=\left ( \frac{5}{n} \right )\:\:\:\:\:\:\:\:\:\:n=height\\\\\:2-\sqrt{3}=\frac{5}{n}$

$\\n=\frac{5}{2-\sqrt3}\times\frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{5(2+\sqrt{3})}{(1)}\\\\\:n=5\left ( 2+\sqrt{3} \right )$

Option 1)

$5(2+\sqrt{3})$

Option 2)

$5(\sqrt{3}+1)$

Option 3)

$\frac{5}{2}(2+\sqrt{3})$

Option 4)

$10(\sqrt{3}-1)$

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