Question

A balloon moving in a straight line passes vertically above two points $A$ and $B$ on horizontal plane $1000ft$ apart. When above $A$ it has an altitude of ${60}^0$ as seen from $B$. When above $B$ it has an altitude of ${45}^0$ as seen from $A$. The distance of $B$ from the point at which it will touch the plane is

• A. $500(\sqrt{3}+1)ft$
• B. $1500ft$
• C. $500(3+\sqrt{3})ft$
• D. $500ft$

Answer 1

The correct option is A $500(\sqrt{3}+1)ft$

tan 60=$=\frac{h}{1000}$
$h=1000\sqrt{3}$
$\frac{1000\sqrt{3}}{1000+x}=\frac{1000}{4}$
$x^2=\frac{1000}{(\sqrt{3}-1)}$
$x^2=500(\sqrt{3}+1)$