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To find the length of the arc \( AB \) for sector \( OAB \), we use the following formula for the length of an arc in a sector:

\[
L = \theta \times r
\]

Where:
- \( L \) is the length of the arc
- \( \theta \) is the angle in radians
- \( r \) is the radius of the circle

### Step 1: Convert the angle from degrees to radians
The given angle is \( 66^\circ \). We need to convert this to radians. The conversion is done by the formula:

\[
\theta \ (\text{in radians}) = \theta \ (\text{in degrees}) \times \frac{\pi}{180}
\]

\[
\theta = 66^\circ \times \frac{\pi}{180} = \frac{66\pi}{180} = \frac{11\pi}{30} \ \text{radians}
\]

### Step 2: Apply the formula for arc length
Now that we have \( \theta = \frac{11\pi}{30} \ \text{radians} \) and the radius \( r = 47 \ \text{mm} \), we can plug these into the arc length formula:

\[
L = \frac{11\pi}{30} \times 47
\]

Let me compute this.The length of the arc \( AB \) is approximately \( 54.1 \ \text{mm} \) to 1 decimal place.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would you calculate the area of sector \( OAB \)?
2. If the angle \( \theta \) was doubled, what would be the new length of arc \( AB \)?
3. How would the arc length change if the radius was halved?
4. Can you find the circumference of the entire circle given the radius?
5. What is the relationship between the arc length and the angle of the sector?

**Tip:** Remember that the arc length depends linearly on both the radius and the central angle (in radians).

Work out the length of the arc AB. Angle OAB is 66°, and the radius of the circle is 47 mm.

Learn how to calculate the length of arc AB in a sector of a circle. This problem involves geometry concepts such as arc length and radian conversions, with a 66-degree angle and a 47mm radius. Suitable for students in Grades 9-11.

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