A kite is flying at a height of $\displaystyle 60$ m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as $\displaystyle 30$°. From the bottom of the same building, the angle of elevation of kite is $\displaystyle 45$°. Find the length of the string and height of roof from the ground. (Use $\displaystyle \sqrt{3}=1.73$ )

Let K be the position of kite and TR is the height of building.$\displaystyle \therefore \tan 45^{0}=1=\frac{60}{\mathrm{GT}}$ $\displaystyle \Rightarrow \mathrm{GT}=60 \mathrm{~m}$ Also, $\displaystyle \tan 30^{0}=\frac{1}{\sqrt{3}}=\frac{\mathrm{KS}}{\mathrm{SR}}$ $\displaystyle \Rightarrow \mathrm{KS}=20 \sqrt{3} \mathrm{~m}$ or $\displaystyle 34.6$ m Hence, $\displaystyle \mathrm{TR}=(60-20 \sqrt{3}) \mathrm{m}=60-34.6=25.4 \mathrm{~m}$ Also, $\displaystyle \sin 30^{0}=\frac{1}{2}=\frac{\mathrm{KS}}{\mathrm{KR}}=\frac{20 \sqrt{3}}{\mathrm{KR}}$ $\displaystyle \Rightarrow \mathrm{KR}=40 \sqrt{3}=69.2 \mathrm{~m}$ ∴ Length of the string $\displaystyle =69.2 \mathrm{~m}$ and height of roof from the ground $\displaystyle =25.4 \mathrm{~m}$