Question

what is the approximate length of arc s on the circle below? use 3.14 for π. round your answer to the nearest tenth.

(image of a circle with a central angle of 330° and radius 12 ft, and arc s labeled)

options:
5.8 ft
6.3 ft
27.5 ft
69.1 ft

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) is \( s=\frac{\theta}{360^{\circ}}\times2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify values

Here, \( \theta = 330^{\circ} \), \( r = 12 \) ft, and \( \pi\approx3.14 \).

Step3: Substitute into formula

First, calculate \( 2\pi r \): \( 2\times3.14\times12 = 75.36 \) ft (this is the circumference of the circle).
Then, find the fraction of the circle corresponding to the arc: \( \frac{330^{\circ}}{360^{\circ}}=\frac{11}{12} \).
Multiply this fraction by the circumference: \( s=\frac{11}{12}\times75.36 \).
Calculate \( \frac{11}{12}\times75.36 = 11\times6.28 = 69.08 \approx 69.1 \) ft.

Answer:

69.1 ft