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The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

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$\frac{5}{2} \sqrt{5}$

$5 \sqrt{5}$

answer is A.

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Detailed Solution

$\tan 45^{0} = \frac{OP}{OA} \Rightarrow OA = 5 \tan 30^{0} = \frac{OP}{OB} \Rightarrow OB = 5 \sqrt{3} AB = \sqrt{{OA}^{2} + {OB}^{2}} = 10$

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