To find the length of an arc subtended by a central angle, we can use the formula:

$L = 2\pi r \times \left( \frac{\theta}{360} \right)$

Where:

• $L$ is the length of the arc
• $r$ is the radius of the circle
• $\theta$ is the central angle in degrees
• $\pi$ is approximately 3.1416

Given:

• Radius $r = 15 \, \text{cm}$
• Central angle $\theta = 85^\circ$

Now, substitute the values into the formula:

$L = 2\pi \times 15 \times \left( \frac{85}{360} \right)$

First, simplify the expression inside the parentheses:

$\frac{85}{360} \approx 0.2361$

Now, multiply:

$L = 2 \times 3.1416 \times 15 \times 0.2361 \approx 22.276 \, \text{cm}$

Rounding to the nearest tenth:

$L \approx 22.3 \, \text{cm}$

Thus, the length of the arc is approximately 22.3 cm.

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:

1. How would the formula change if the central angle was given in radians instead of degrees?
2. What would the arc length be if the central angle were doubled?
3. How can you derive the arc length formula from the circumference formula of a circle?
4. What is the difference between an arc length and the chord length of the same angle?
5. How would the arc length change if the radius of the circle were halved?

Tip: Remember that arc length is proportional to both the radius of the circle and the central angle!