Question

Two rays are drawn through a point $A$ at an angle of ${30}^o.$ A point $B$ is taken on one of them at distance $a$ from the point $A$. A perpendicular is drawn from the point $B$ to the other ray. Another perpendicular is drawn from its foot to $AB$, and so on then the length of the resulting infinite polygonal line is

• A. $2\sqrt{3}a$
• B. $a(2+\sqrt{3})$
• C. $a(2-\sqrt{3})$
• D. None of these

Answer 1

The correct option is B $a(2+\sqrt{3})$

$a\sin {30}^o+a\sin {30}^o\cos 30+a\sin 30(cos{30}^o{)}^2+$......

$Sum=\frac{A}{1-r}$

$r=\cos {30}^{\circ }$ and $A=a\sin 30.$

$=\frac{a\sin {30}^{\circ }}{1-\cos {30}^{\circ }}$

$=\frac{a}{(2-\sqrt{3})}$

$=a(2+\sqrt{3})$