Question

question 1 (1 point)
length of arc de = ______ yd

question 2 (1 point)
length of arc lm = ______ ft

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify given values

Here, the radius \( r = 8 \) yd and the central angle \( \theta = 160^\circ \).

Step3: Substitute values into formula

Substitute \( \theta = 160^\circ \) and \( r = 8 \) into the formula:
\( L = \frac{160^\circ}{360^\circ} \times 2\pi \times 8 \)
Simplify \( \frac{160}{360} = \frac{4}{9} \), so:
\( L = \frac{4}{9} \times 16\pi \)
\( L = \frac{64\pi}{9} \approx \frac{64\times3.1416}{9} \approx \frac{201.0624}{9} \approx 22.34 \) (or keep it as \( \frac{64\pi}{9} \))

Answer:

\(\frac{64\pi}{9}\) (or approximately \(22.34\))