To solve this problem, we can use trigonometry. Let's break it down into smaller steps:

Step 1: Draw a diagram

First, let's draw a diagram to visualize the problem. We have a kite flying at a height of 100 meters above the ground, forming an angle of 60 degrees with the ground.

Step 2: Identify the relevant trigonometric ratio

Since we have the angle and the opposite side length (the height of the kite), we can use the sine function to solve this problem.

Step 3: Apply the sine function

According to the sine function, sin(angle) = opposite/hypotenuse. In this case, the opposite side is the height of the kite (100 meters) and the hypotenuse is the length of the kite string that we need to find.

So, sin(60 degrees) = 100/hypotenuse.

Step 4: Solve for the hypotenuse

To solve for the hypotenuse, we need to isolate it in the equation. We can do this by multiplying both sides of the equation by the hypotenuse:

hypotenuse * sin(60 degrees) = 100.

Step 5: Calculate the hypotenuse

To find the hypotenuse, we need to evaluate sin(60 degrees). The sine of 60 degrees is √3/2.

So, hypotenuse * (√3/2) = 100.

Now, we can solve for the hypotenuse:

hypotenuse = 100 / (√3/2).

hypotenuse = 100 * (2/√3).

hypotenuse = (200/√3).

hypotenuse = (200/√3) * (√3/√3).

hypotenuse = (200√3) / 3.

Therefore, the length of the kite string is (200√3) / 3 meters.

Step 6: Simplify the answer

To simplify the answer, we can multiply both the numerator and denominator by √3:

(200√3) / 3 = (200√3 * √3) / (3 * √3).

(200√3) / 3 = (200 * 3) / (3√3).

(200√3) / 3 = 600 / (3√3).

(200√3) / 3 = 200 / √3.

Therefore, the length of the kite string is 200 / √3 meters.

Step 7: Rationalize the denominator

To rationalize the denominator, we can multiply both the numerator and denominator by √3:

(200 / √3) * (√3 / √3) = (200√3) / 3.

Therefore, the length of the kite string is (200√3) / 3 meters.

So, the correct answer is option c) \(25 \sqrt{3}\) meters.

## Answers & Comments

To solve this problem, we can use trigonometry. Let's break it down into smaller steps:

Step 1: Draw a diagram

First, let's draw a diagram to visualize the problem. We have a kite flying at a height of 100 meters above the ground, forming an angle of 60 degrees with the ground.

Step 2: Identify the relevant trigonometric ratio

Since we have the angle and the opposite side length (the height of the kite), we can use the sine function to solve this problem.

Step 3: Apply the sine function

According to the sine function, sin(angle) = opposite/hypotenuse. In this case, the opposite side is the height of the kite (100 meters) and the hypotenuse is the length of the kite string that we need to find.

So, sin(60 degrees) = 100/hypotenuse.

Step 4: Solve for the hypotenuse

To solve for the hypotenuse, we need to isolate it in the equation. We can do this by multiplying both sides of the equation by the hypotenuse:

hypotenuse * sin(60 degrees) = 100.

Step 5: Calculate the hypotenuse

To find the hypotenuse, we need to evaluate sin(60 degrees). The sine of 60 degrees is √3/2.

So, hypotenuse * (√3/2) = 100.

Now, we can solve for the hypotenuse:

hypotenuse = 100 / (√3/2).

hypotenuse = 100 * (2/√3).

hypotenuse = (200/√3).

hypotenuse = (200/√3) * (√3/√3).

hypotenuse = (200√3) / 3.

Therefore, the length of the kite string is (200√3) / 3 meters.

Step 6: Simplify the answer

To simplify the answer, we can multiply both the numerator and denominator by √3:

(200√3) / 3 = (200√3 * √3) / (3 * √3).

(200√3) / 3 = (200 * 3) / (3√3).

(200√3) / 3 = 600 / (3√3).

(200√3) / 3 = 200 / √3.

Therefore, the length of the kite string is 200 / √3 meters.

Step 7: Rationalize the denominator

To rationalize the denominator, we can multiply both the numerator and denominator by √3:

(200 / √3) * (√3 / √3) = (200√3) / 3.

Therefore, the length of the kite string is (200√3) / 3 meters.

So, the correct answer is option c) \(25 \sqrt{3}\) meters.