A kite is flying at a height of 60m 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 60°. Find the length of the string, assuming that there is no slack in the string.

Step 1: Identify the given information and the unknown

We are given the height at which the kite is flying, which forms the perpendicular side of a right-angled triangle. The angle of inclination of the string with the ground is also given. We need to find the length of the string, which represents the hypotenuse of this right-angled triangle.

Step 2: Formulate the trigonometric relationship

In the right-angled triangle formed by the kite, the string, and the ground, the height of the kite is the perpendicular side opposite to the angle of inclination, and the length of the string is the hypotenuse. The sine function relates the perpendicular side to the hypotenuse.

Step 3: Substitute values and solve for the length of the string

We substitute the known values into the sine equation. We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$. Then, we solve for AC by isolating it. To rationalize the denominator, we multiply both the numerator and denominator by $\sqrt{3}$.

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