In a circle of radius 5, the length of the arc that subtends a central angle of 159 degrees is 

To find the length of an arc that subtends a central angle in a circle, we use the formula:

\[
\text{Arc Length} = r \theta
\]

where:
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle in radians.

### Step 1: Convert the angle from degrees to radians
Since the given central angle is in degrees, we first convert it to radians:

\[
\theta = 159^\circ \times \frac{\pi}{180^\circ} = \frac{159\pi}{180} = \frac{53\pi}{60} \, \text{radians}
\]

### Step 2: Calculate the arc length
Now, substitute the radius \( r = 5 \) and the angle \( \theta = \frac{53\pi}{60} \) into the formula:

\[
\text{Arc Length} = 5 \times \frac{53\pi}{60} = \frac{53\pi}{12}
\]

### Step 3: Approximate the arc length
To approximate the arc length, use \( \pi \approx 3.1416 \):

\[
\text{Arc Length} \approx \frac{53 \times 3.1416}{12} \approx 13.86 \, \text{units}
\]

Thus, the length of the arc is approximately **13.86 units**.

Would you like more details or have any questions?

### Related questions:
1. How do you convert angles between degrees and radians?
2. What is the formula for the circumference of a circle, and how does it relate to arc length?
3. How would the arc length change if the radius were doubled?
4. What is the relationship between arc length and sector area in a circle?
5. How does the central angle affect the length of the arc in a circle?

### Tip:
Always make sure to convert angles to radians when working with circular arc lengths or sector areas in most mathematical formulas!

In a circle of radius 5, the length of the arc that subtends a central angle of 159 degrees is

Learn how to calculate the arc length in a circle with a radius of 5 units and a central angle of 159 degrees. This problem demonstrates key concepts in geometry, including radians and arc length formulas. Suitable for students in Grades 9-10.

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