Isabelle is flying a kite on a windy day. When the kite is 15 m above ground, it makes an angle of 50° with the horizontal. If Isabelle is holding the string 1 m above the ground, how much string has she released? Round your answer to the nearest metre.

To determine how much string Isabelle has released, we can model the situation using a right triangle:

- **Height of the kite above Isabelle's hand**: Since the kite is 15 m above the ground and Isabelle is holding the string 1 m above the ground, the vertical height we consider is:  
  \[
  h = 15 - 1 = 14 \, \text{m}.
  \]

- **Angle of elevation**: The kite string makes an angle of \( 50^\circ \) with the horizontal.

- **Hypotenuse**: The string forms the hypotenuse of the right triangle.

---

### Step 1: Using the sine function
In a right triangle, the sine of an angle is defined as:  
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}.
\]
Here:
- \( \theta = 50^\circ \) (angle of elevation),
- opposite = 14 m (vertical height from Isabelle's hand to the kite),
- hypotenuse = \( L \) (the length of the string).

Substitute into the formula:  
\[
\sin(50^\circ) = \frac{14}{L}.
\]

---

### Step 2: Solving for \( L \) (the string length)
Rearranging for \( L \):  
\[
L = \frac{14}{\sin(50^\circ)}.
\]

Using a calculator:  
- \( \sin(50^\circ) \approx 0.7660 \).

Now substitute:  
\[
L = \frac{14}{0.7660} \approx 18.28 \, \text{m}.
\]

---

### Step 3: Rounding
Rounding to the nearest metre:  
\[
L \approx 18 \, \text{m}.
\]

---

### Final Answer:
Isabelle has released approximately **18 metres** of string.

---

### Do you want further clarification or a diagram? Let me know!  
Here are 5 related questions to explore:  
1. What is the length of the string if the angle of elevation changes to \( 60^\circ \)?  
2. How high would the kite be if Isabelle released 20 m of string at the same angle?  
3. If the wind lifts the kite to \( 20 \, \text{m} \) above the ground, what is the new angle of elevation?  
4. What is the horizontal distance from Isabelle to the kite in this problem?  
5. How would the solution change if Isabelle were holding the string at ground level?

**Tip**: For right triangle problems, trigonometric ratios (sine, cosine, and tangent) are key tools!

Solve a real-world trigonometry problem involving a kite flying at a height of 15 meters with a 50° angle of elevation. Learn to calculate the string length using sine functions and trigonometric ratios, perfect for Grades 9-10 students.

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