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# 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.

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

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

$$x \ = \ \frac{120}{ \sqrt{3}} \ = \ 40 \sqrt{3}$$

$$\therefore$$ the length of the string is $$40 \sqrt{3}$$ m