Question

A boy is standing on the ground and flying a kite with 120 m of string at an elevation of ${30}^{\circ }$. Another boy is standing on the roof of a 20 m high building and is flying his kite at an elevation of ${60}^{\circ }$. The kites are flying towards each other and the boys are on opposite sides of both the kites. The length of string that the second boy must have so that the two kites meet is

• A. $48\frac{\sqrt{3}}{3}$
• B. $15\sqrt{3}m$
• C. $70\sqrt{3}m$
• D. $80\frac{\sqrt{3}}{3}$

Answer 1

The correct option is D $80\frac{\sqrt{3}}{3}$


$DE=lsin{60}^{\circ }$
$EF=20m$
$DF=120sin{30}^{\circ }$
$=lsin{60}^{\circ }+20$
$\therefore l=\frac{120sin{30}^{\circ }-20}{sin{60}^{\circ }}m$
$=\frac{(60-20)\times 2}{\sqrt{3}}=80\frac{\sqrt{3}}{3}m$