To solve this, we use trigonometry. Specifically, the kite, the string, and the ground form a right triangle where:

• The height of the kite ($h$) is one leg of the triangle: $h = 30 \, \text{m}$,
• The string of the kite ($s$) is the hypotenuse,
• The angle between the string and the ground is $45^\circ$.

Step-by-step solution:

1. Identify the trigonometric relation:
   Since we have the opposite side ($h$) and need the hypotenuse ($s$), we use the sine function:
   $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

2. Substitute the known values:
   $\sin(45^\circ) = \frac{30}{s}$
   The value of $\sin(45^\circ)$ is $\frac{\sqrt{2}}{2}$ (approximately 0.7071).

3. Solve for $s$:
   $\frac{\sqrt{2}}{2} = \frac{30}{s} \quad \Rightarrow \quad s = \frac{30}{\frac{\sqrt{2}}{2}} = 30 \times \frac{2}{\sqrt{2}} = 30 \sqrt{2}$

4. Simplify the result:
   $s \approx 30 \times 1.414 \approx 42.43 \, \text{m}$

Final Answer:

The length of the string is approximately 42.43 meters.

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Would you like me to explain any step in more detail?

Related Questions:

1. How does the sine function relate to angles in a triangle?
2. Can you use the cosine function to solve this problem?
3. What is the exact length of the string if more precision is needed?
4. How does the answer change if the angle is 30° instead of 45°?
5. What assumptions are made in solving this problem?

Tip:

Always double-check the angle and which trigonometric ratio fits the given information when solving geometry problems involving triangles.