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Q5. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60º. Find the length of the string, assuming that there is no slack in the string.
Answer :


Let OA be the horizontal ground, and let K be the position of the kite at height 60 m above the ground. Let the length of the string OK be x metres. It is given \( ∠ \ KOA \ = \ 60º \)



In \( ∆ \ AOK \), we have

\( \frac{AK}{OK} \ = \ sin60º \ => \ \frac{60}{x} \ = \ \frac{ \sqrt{3}}{2} \)

\( x \ = \ \frac{120}{ \sqrt{3}} \ = \ 40 \sqrt{3} \)

∴ the length of the string is \( 40 \sqrt{3} \) m