Explanation:

To find the length of the string, we can use trigonometry. The height of the kite forms the opposite side of a right triangle, and the string is the hypotenuse. The given angle is 60 degrees.

- Trigonometric Relationship: Use the sine function:

$$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$

- Calculation:

$$\sin(60^\circ) = \frac{123}{\text{length of string}}$$

$$0.866 \approx \frac{123}{\text{length of string}}$$

$$\text{length of string} \approx \frac{123}{0.866} \approx 142$$

- Options:

- Option 1: 140 m: Too short.

- Option 2: 139 m: Too short.

- Option 3: 142 m: Matches calculation.

- Option 4: 138 m: Too short.

- Conclusion:

- Option 3: 142 m is correct.