A kite is attached to a string. Find the length of the string , when the height of the kite is 60 m and the string makes an angle `30^(@)` with the ground .

Answer

To find the length of the string attached to the kite, we can use trigonometric ratios. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a kite at a height of 60 meters, and the string makes an angle of 30 degrees with the ground. We need to find the length of the string.

### Step 2: Draw a Diagram
Draw a right triangle where:
- Point A is the position of the kite.
- Point B is the point on the ground directly below the kite.
- Point C is the point where the string is attached to the ground.

In this triangle:
- AB (height of the kite) = 60 m
- Angle ABC = 30 degrees
- AC (length of the string) is what we need to find.

### Step 3: Use Trigonometric Ratios
In a right triangle, we can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
Here, the opposite side is AB (height of the kite) and the hypotenuse is AC (length of the string).

### Step 4: Set Up the Equation
Using the sine function:
\[ \sin(30^\circ) = \frac{AB}{AC} \]
Substituting the known values:
\[ \sin(30^\circ) = \frac{60}{AC} \]

### Step 5: Calculate the Value of Sine
We know that:
\[ \sin(30^\circ) = \frac{1}{2} \]
So, substituting this into the equation gives:
\[ \frac{1}{2} = \frac{60}{AC} \]

### Step 6: Solve for AC
Cross-multiplying to solve for AC:
\[ AC \cdot \frac{1}{2} = 60 \]
\[ AC = 60 \cdot 2 \]
\[ AC = 120 \text{ m} \]

### Conclusion
The length of the string is 120 meters.

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