Question

R=10 angle is 70, what is length of arc

Answer 1

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**.