A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°. Another boy standing on the roof…

Let K be the position of kite. Let \(\displaystyle \mathrm{KL}=\mathrm{h}, \mathrm{CP}=x \& \mathrm{~PB}=y\) In rt. angled \(\displaystyle \triangle \mathrm{KPB}\) \[\frac{\mathrm{h}+20}{60}=\sin 30^{\circ}=\frac{1}{2} \] \(\displaystyle \Rightarrow \mathrm{h}=10\) Also, \(\displaystyle \frac{\mathrm{y}}{60}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) \(\displaystyle \Rightarrow \mathrm{y}=30 \sqrt{3}=30 \times 1.73=51.9\) In rt. angled \(\displaystyle \Delta \mathrm{KLM}\) \[\frac{10}{x}=\tan 45^{\circ}=1 \] \(\displaystyle \Rightarrow x=10\) Height of kite from ground is \(\displaystyle 10+20=30 \mathrm{~m}\) Distance of first boy from the base of the building \(\displaystyle =51.9+10=61.9 \mathrm{~m}\)