The angle of elevation of the top P of a towe | vedclass

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(A) Let the height of the tower be $h = 5 	ext{ m}$. Let the base of the tower be $O$. Let the position of the first person be $A$ (South) and the se

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$10$

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(A) Let the height of the tower be $h = 5 	ext{ m}$. Let the base of the tower be $O$. Let the position of the first person be $A$ (South) and the second person be $B$ (West).In $	riangle POA$,$	an(45^{\circ}) = \frac{PO}{OA} \implies 1 = \frac{5}{OA} \implies OA = 5 	ext{ m}$.In $	riangle POB$,$	an(30^{\circ}) = \frac{PO}{OB} \implies \frac{1}{\sqrt{3}} = \frac{5}{OB} \implies OB = 5\sqrt{3} 	ext{ m}$.Since the directions South and West are perpendicular,$	riangle AOB$ is a right-angled triangle at $O$.The distance between the two persons is $AB = \sqrt{OA^2 + OB^2} = \sqrt{5^2 + (5\sqrt{3})^2} = \sqrt{25 + 75} = \sqrt{100} = 10 	ext{ m}$.

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