MCQ
A balloon moving in a straight line passes vertically above two points $A$ and $B$ on horizontal plane $1000$ ft apart. When above $A$ it has an altitude of $60^\circ$ as seen from $B$. When above $B$ it has an altitude of $45^\circ$ as seen from $A$. The distance of $B$ from the point at which it will touch the plane is :
  • $500(\sqrt{3}+1)\text{ft}$
  • B
    $1500\text{ ft}$
  • C
    $500(3+\sqrt{3})\text{ ft}$
  • D
    $500\text{ ft}$

Answer

Correct option: A.
$500(\sqrt{3}+1)\text{ft}$
$\tan60=\frac{\text{h}}{1000}$
$\text{h}=1000\sqrt{3}$
$\frac{1000\sqrt{3}}{1000+\text{x}}=\frac{1000}{4}$
$\text{x}^2=\frac{1000}{(\sqrt{3}-1)}$
$\text{x}^2=500(\sqrt{3}+1)$

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