To find the length of an arc given the radius of the circle and the angle it subtends in radians, we can use the formula:
[tex]\[ \text{arc length} = \text{radius} \times \text{angle in radians} \][/tex]
In this problem, the given values are:
- Radius ([tex]\( r \)[/tex]) = 13 cm
- Angle ([tex]\( \theta \)[/tex]) = 0.9 radians
Substitute the given values into the formula:
[tex]\[ \text{arc length} = 13 \, \text{cm} \times 0.9 \, \text{radians} \][/tex]
Now, calculate the arc length:
[tex]\[ \text{arc length} = 11.7 \, \text{cm} \][/tex]
Thus, the length of the arc is 11.7 cm.
