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 $180^\circ = \pi \, \text{radians}$.