A kite is flown with a thread of 250 m length. If the thread is assumed to be stretched and makes an angle of `60^(@)` with the horizontal, then the height of the kite above the ground is (approx.) :

Options

A. 216.25 m
B. 215.25 m
C. 212.25 m
D. 210.25 m

Answer

To find the height of the kite above the ground, we can use basic trigonometry. Here's the step-by-step solution:

### Step 1: Understand the problem
We have a kite being flown with a thread of length 250 meters, making an angle of 60 degrees with the horizontal. We need to find the vertical height of the kite above the ground.

### Step 2: Draw a diagram
Visualize the situation:
- Draw a horizontal line representing the ground.
- Draw a vertical line representing the height of the kite.
- Draw the kite and the thread making an angle of 60 degrees with the horizontal.

### Step 3: Identify the right triangle
The thread forms a right triangle with:
- The length of the thread as the hypotenuse (250 m).
- The height of the kite as the opposite side to the angle (60 degrees).
- The horizontal distance as the adjacent side.

### Step 4: Use the sine function
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can write:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
For our case:
\[ \sin(60^\circ) = \frac{\text{Height}}{250} \]

### Step 5: Substitute the values
We know that:
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]
Now, substituting this into the equation:
\[ \frac{\sqrt{3}}{2} = \frac{\text{Height}}{250} \]

### Step 6: Solve for the height
To find the height, we can rearrange the equation:
\[ \text{Height} = 250 \cdot \frac{\sqrt{3}}{2} \]
Calculating this gives:
\[ \text{Height} = 250 \cdot 0.866 \approx 216.5 \text{ meters} \]

### Step 7: Final calculation
To be more precise, using the exact value of \(\sqrt{3} \approx 1.732\):
\[ \text{Height} = 250 \cdot \frac{1.732}{2} = 250 \cdot 0.866 = 216.5 \text{ meters} \]

### Conclusion
Thus, the height of the kite above the ground is approximately **216.5 meters**.

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