a kite flying a height of 70m is attached to a string inclinedat 44° to the horizontal.What is the length of the string?

To determine the length of the string, we can use trigonometry. Specifically, the sine function is appropriate here because it relates the angle of inclination, the height (opposite side), and the length of the string (hypotenuse).

Given:
- Height of the kite (\( h \)) = 70 meters
- Angle of inclination (\( \theta \)) = 44°

We need to find the length of the string (\( L \)).

The sine of the angle is given by:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}
\]

Rearranging to solve for \( L \):
\[
L = \frac{h}{\sin(\theta)}
\]

Substituting the known values:
\[
L = \frac{70}{\sin(44^\circ)}
\]

Now, let's calculate the value of \( L \).

\[
L \approx \frac{70}{0.6947} \approx 100.8 \text{ meters}
\]

So, the length of the string is approximately **100.8 meters**.

Would you like further details or have any questions about this calculation?

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Here are five related questions:
1. What if the angle of inclination was 60°? How would the string length change?
2. How would the length change if the kite was flying at a height of 100 meters with the same angle?
3. What is the relationship between the angle of inclination and the length of the string?
4. Can we calculate the horizontal distance from the point where the string is tied to the ground to the point directly below the kite?
5. What would be the length of the string if the kite's height was doubled, keeping the angle the same?

**Tip:** Remember that in right-angled triangles, the sine function is very useful for relating angles to the ratio of the opposite side over the hypotenuse.

Learn how to calculate the length of a kite string attached at a 44° angle to the horizontal, flying at a height of 70 meters. Using trigonometry and the sine function, discover the method to find the string length accurately. Suitable for high school students studying trigonometry.

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