Carol is flying a kite on level ground, and the string forms an angle of 50

To solve these problems, we can use trigonometry and the information provided in the problem.

### Given information:
- Angle of the kite with the ground: 50°
- Angle of elevation from the two friends to the kite: 66° and 35°
- Distance of one friend from Carol: 11 m

First, we will calculate how high the kite is above the ground, how long the string is, and how far the other friend is from Carol.

#### Step 1: Find the height of the kite above the ground (h).

Let \( D \) be the horizontal distance from Carol to the point directly below the kite, and \( L \) be the length of the kite string.

Using the angle formed by the string with the ground (50°):
- The height of the kite \( h \) can be expressed as:
\[ h = L \sin(50°) \]

Using the angle of elevation from Friend 1 (66°) and the distance from Carol (11 m):
\[ h = 11 \tan(66°) \]

Now we can calculate this height:

- Calculate \( h \):
\[ h = 11 \tan(66°) \approx 11 \times 2.244 = 24.684 \approx 25 \, \text{m} \]

#### Conclusion for a):
**a)** The height of the kite above the ground is approximately 25 m.

#### Step 2: Find the length of the string (L).

We already know \( h = L \sin(50°) \).
From our previous calculation, \( h \approx 25 \, m \).

Now we can calculate \( L \):
\[ L = \frac{h}{\sin(50°)} \]
\[ L = \frac{25}{\sin(50°)} \]
\[ \sin(50°) \approx 0.766 \]
So,
\[ L \approx \frac{25}{0.766} ≈ 32.6 \approx 33 \, \text{m} \]

#### Conclusion for b):
**b)** The length of the string is approximately 33 m.

#### Step 3: Find the distance of the other friend from Carol.

Using the angle of elevation from Friend 2 (35°):
Let \( d \) be the distance from Friend 2 to Carol.

\[ h = d \tan(35°) \]
Since we already know \( h \approx 25 \, m \):
\[ 25 = d \tan(35°) \]
Thus,
\[ d = \frac{25}{\tan(35°)} \]
Where \( \tan(35°) \approx 0.700 \):
\[ d \approx \frac{25}{0.700} \approx 35.71 \approx 36 \, m \]

#### Conclusion for c):
**c)** The distance of the other friend from Carol is approximately 36 m.

To summarize:
1. **Height of the kite**: ≈ 25 m
2. **Length of the string**: ≈ 33 m
3. **Distance of the other friend**: ≈ 36 m