Find the arclength along a circle of radius 5.3 inches which subtends an angle of \( 275^{\circ} \) Give your answer accurate to the nearest tenth of an inch. in.

To find the arclength \( L \) along a circle, we can use the formula \( L = r \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians. First, we need to convert the angle from degrees to radians. \[ \theta = 275^{\circ} \times \frac{\pi}{180^{\circ}} \approx 4.791 \text{ radians} \] Now, substituting the values into the arclength formula: \[ L = 5.3 \text{ inches} \times 4.791 \approx 25.4 \text{ inches} \] Thus, the arclength is approximately 25.4 inches when rounded to the nearest tenth. Feeling confused about radians and degrees? You're not alone! A common mistake is to forget to convert angles into radians when using the arclength formula. Always remember that radians are the units matched with the arc length formula, because they're based on the circle's radius—saving you a lot of headaches during calculations! If you want to dive deeper into understanding circles and their properties, there are fantastic resources out there. Books about trigonometry or even engaging online courses can offer the perfect mix of theory and practice. Embrace the journey of learning more about circles, and you'll find it rewarding in various applications from engineering to art!