A kite is flying at an inclination of `60^@` with the horizontal. If the length of the thread is 120 m, then the height of the kite is

Options

A. `60sqrt3m`
B. 60 m
C. `60sqrt3m`
D. 120 m

Answer

To find the height of the kite flying at an inclination of \(60^\circ\) with the horizontal, we can use trigonometric functions. The length of the thread acts as the hypotenuse of a right triangle, where the height of the kite is the opposite side to the angle of inclination.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the thread (hypotenuse) = 120 m
- Angle of inclination with the horizontal = \(60^\circ\)

2. **Use the Sine Function:**
The height of the kite can be found using the sine function, which relates the opposite side (height of the kite) to the hypotenuse (length of the thread):
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
Here, \(\theta = 60^\circ\), and the hypotenuse is 120 m.

3. **Set Up the Equation:**
\[ \sin(60^\circ) = \frac{\text{Height}}{120} \]

4. **Calculate \(\sin(60^\circ)\):**
We know that:
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]

5. **Substitute and Solve for Height:**
\[ \frac{\sqrt{3}}{2} = \frac{\text{Height}}{120} \]
Multiplying both sides by 120:
\[ \text{Height} = 120 \cdot \frac{\sqrt{3}}{2} \]
\[ \text{Height} = 60\sqrt{3} \text{ m} \]

6. **Final Calculation:**
To get a numerical value, we can approximate \(\sqrt{3} \approx 1.732\):
\[ \text{Height} \approx 60 \cdot 1.732 \approx 103.92 \text{ m} \]

### Conclusion:
The height of the kite is approximately \(60\sqrt{3} \approx 103.92\) meters.