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The problem asks for the radian measure of the central angle \( \theta \) that intercepts an arc of length 9 feet in a circle with a radius of 11 feet.

The formula to find the central angle \( \theta \) in radians is:

\[
\theta = \frac{s}{r}
\]

Where:
- \( s \) is the arc length,
- \( r \) is the radius of the circle.

### Substituting the values:
- \( s = 9 \, \text{ft} \),
- \( r = 11 \, \text{ft} \).

\[
\theta = \frac{9}{11} \approx 0.8182 \, \text{radians}
\]

Rounding the answer to the nearest tenth:

\[
\theta \approx 0.8 \, \text{radians}
\]

Let me know if you'd like further details or clarifications!

### Here are 5 related questions for further practice:
1. What is the central angle in radians if the arc length is 15 feet and the radius is 12 feet?
2. How do you convert radians to degrees for a given angle?
3. If the radius is doubled, how does that affect the radian measure of the central angle for a fixed arc length?
4. What is the formula for finding the arc length given the central angle in degrees?
5. How would the central angle change if the arc length is halved but the radius remains the same?

#### Tip: When working with radians and degrees, remember that \( 180^\circ = \pi \) radians!

A circle has a radius of 11 ft. Find the radian measure of the central angle θ that intercepts an arc of length 9 ft.

Learn how to find the radian measure of a central angle θ in a circle with a radius of 11 ft that intercepts an arc of 9 ft. This problem involves the arc length formula and understanding radians.

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