To find the length of an arc, you can use the formula:
\[ \text{Arc Length} = R \times \theta \]
where:
- \( R \) is the radius of the circle,
- \( \theta \) is the angle in radians.
First, you need to convert the angle from degrees to radians. The conversion is given by:
\[ \theta , \text{(radians)} = \theta , \text{(degrees)} \times \frac{\pi}{180} \]
For an angle of 70 degrees:
\[ \theta = 70 \times \frac{\pi}{180} = \frac{70\pi}{180} = \frac{7\pi}{18} \text{ radians} \]
Now plug in the radius \( R = 10 \) and the angle in radians into the arc length formula:
\[ \text{Arc Length} = 10 \times \frac{7\pi}{18} \]
Calculating this gives:
\[ \text{Arc Length} = \frac{70\pi}{18} = \frac{35\pi}{9} \text{ units} \]
Thus, the length of the arc is approximately:
\[ \frac{35\pi}{9} \approx 12.27 \text{ units (using } \pi \approx 3.14\text{)} \]
So, the arc length is approximately 12.27 units.