question_answer

Amit is standing on the ground and flying a kite with 100 m of string at an elevation of \[{{30}^{o}}\]. Another boy, Nitin is standing on the roof of a 10 m high building and is flying his kite at an elevation of \[{{45}^{o}}\]. Both Amit and Nitin are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.

A)  \[40\sqrt{2}\,m\]       

B)  \[50\sqrt{3}\,m\]        

C)         \[42\sqrt{3}\,m\]       

D)         \[41\sqrt{2}\,m\]                    

Correct Answer: A

Solution :

Let the length of second string be x m. In \[\Delta \,ABC,\] \[\sin {{30}^{o}}=\frac{AC}{AB}\] or \[\frac{1}{2}=\frac{AC}{100}\]\[\Rightarrow \] \[AC=50\,m\] In \[\Delta \,AEF,\]                                     \[\sin {{45}^{o}}=\frac{AF}{AE}\Rightarrow \frac{1}{\sqrt{2}}=\frac{AC-FC}{x}\] \[\Rightarrow \]            \[\frac{1}{\sqrt{2}}=\frac{50-10}{x}\]             \[[\because \,\,AC=50m,\,\,FC=ED=10\,m]\] \[\Rightarrow \]            \[\frac{1}{\sqrt{2}}=\frac{40}{x}\Rightarrow x=40\sqrt{2}m\] So, the length of string that the second boy must have so that the two kites meet \[=40\sqrt{2}\,m\]