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To solve this problem, we will use the formula for the length of an arc \( L \) subtended by a central angle \( \theta \) in a circle of radius \( r \):

\[
L = \frac{\theta}{360} \times 2\pi r
\]

Given:
- \( r = 15 \, \text{cm} \) (radius of the circle),
- \( \theta = 85^\circ \) (central angle),
- \( \pi \approx 3.1416 \).

Now, let's substitute these values into the formula:

\[
L = \frac{85}{360} \times 2 \times 3.1416 \times 15
\]

First, calculate the fraction of the circle's circumference:

\[
L = \frac{85}{360} \times 94.248
\]

\[
L \approx 0.2361 \times 94.248 = 22.24 \, \text{cm}
\]

Thus, the length of the arc is approximately **22.2 cm** (rounded to the nearest tenth).

Would you like further explanation or details?

Here are 5 related questions:
1. How is the formula for the arc length derived?
2. What would the arc length be if the central angle were 180 degrees?
3. How does changing the radius affect the arc length?
4. Can this formula be applied to radians instead of degrees?
5. What is the relationship between the arc length and the sector area?

**Tip:** To convert between degrees and radians, remember that \( 180^\circ = \pi \, \text{radians} \).

On a circle of radius 15 cm, find the length of the arc subtended by a central angle of 85 degrees. Round your answer to the nearest tenth.

Learn how to calculate the length of an arc on a circle with a radius of 15 cm, subtended by a central angle of 85 degrees. This geometry problem involves using the formula L = (θ/360) × 2πr and is suitable for students in Grades 9-11.

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