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

To find the length of the string that is attached to the kite, we use trigonometry. Here's how we approach the problem:

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

### Problem:
We need to find the length of the string (\( L \)), which is the hypotenuse of the right triangle formed by the kite, the ground, and the point where the string is attached.

### Solution:
The sine function relates the angle of inclination, the height of the kite (opposite side), and the length of the string (hypotenuse):

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}
\]

Rearranging to solve for \( L \):

\[
L = \frac{h}{\sin(\theta)}
\]

Substitute the given values:

\[
L = \frac{70}{\sin(44^\circ)}
\]

Now calculate the sine of 44°:

\[
\sin(44^\circ) \approx 0.6947
\]

So,

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

### Answer:
The length of the string is approximately **100.8 meters**.

Would you like more details or have any questions about this solution?

---

Here are five related questions:
1. What would the length of the string be if the angle of inclination was 30°?
2. How would the length of the string change if the kite was at a height of 50 meters instead?
3. What if the kite's string was inclined at 60°? How would that affect the string length?
4. Can we determine the horizontal distance from the kite's point directly below it to the string's attachment point?
5. How would you calculate the angle of inclination if the string's length and height are known?

**Tip:** Always double-check your trigonometric functions and calculations to ensure accuracy when solving problems involving angles and sides.

Discover how to calculate the length of a string attached to a kite flying at 70 meters height with a 44-degree inclination using trigonometry. Detailed step-by-step solution and calculations included.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation