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To determine the area watered by the sprinkler, we need to find the area of a sector of a circle, since the sprinkler waters a section of the circular area.

### Step-by-Step Solution

1. **Identify Given Values:**
   - Radius of the circle \( r = 43 \) feet (the distance the sprinkler sprays).
   - Angle swept by the sprinkler \( \theta = 4.9 \) radians.

2. **Formula for the Area of a Sector:**
   The area \( A \) of a sector with radius \( r \) and angle \( \theta \) (in radians) is given by:
   \[
   A = \frac{1}{2} r^2 \theta
   \]

3. **Substitute Values:**
   \[
   A = \frac{1}{2} \times 43^2 \times 4.9
   \]
   Calculating this step-by-step:
   - \( 43^2 = 1849 \)
   - \( 1849 \times 4.9 = 9060.1 \)
   - \( \frac{1}{2} \times 9060.1 = 4530.05 \)

4. **Final Answer:**
   The area of the lawn that the sprinkler has watered is approximately:
   \[
   4530.05 \text{ square feet}
   \]

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

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### Related Questions
1. How would the area change if the sprinkler covered an angle of 3 radians?
2. What would be the area if the sprinkler distance increased to 50 feet?
3. How is the sector area formula derived?
4. If the sprinkler rotated a full circle, what area would be covered?
5. What happens to the area if the angle decreases by half?

### Tip
Always use radians when calculating sector areas in a circle, as the formula \( A = \frac{1}{2} r^2 \theta \) assumes the angle is in radians.

Suppose the sprinkler has rotated through an angle of 4.9 radians. What area (in square feet) of the lawn has the water covered?

Determine the area covered by a sprinkler rotating through an angle of 4.9 radians with a spray distance of 43 feet. This geometry problem involves finding the sector area of a circle using the formula A = (1/2) * r^2 * θ. Suitable for high school students in Grades 9-12.

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