If the distance between the top of two trees of height 20 m and 28 m is 17 m,

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Question

If the distance between the top of two trees of height 20 m and 28 m is 17 m, then the horizontal distance between the trees is:

Options:

A . 11 m

B . 31 m

C . 15 m

D . 9 m

Answer: Option C
:
C

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

Draw $B E$ parallel to $A C$ . Then,
$E D = 8 m$ .
By applying Pythagoras' theorem,
$B E^{2} + D E^{2} = B D^{2}$ .

$∴ B E = \sqrt{{B D}^{2} - {D E}^{2}} = \sqrt{{(17)}^{2} - 8^{2}}$
$= \sqrt{289 - 64} = \sqrt{225} = 15 m$

$∴ A C = B E = 15 m$

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