Question

graded quiz: circles
0:17:36 elapsed
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the circumference of the circle in the above figure is 128 ft. what is the length of ab?

Explanation:

Step1: Recall the formula for arc length

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times C\), where \(\theta\) is the central angle in degrees and \(C\) is the circumference of the circle.

Step2: Substitute the given values

We are given that \(\theta = 45^{\circ}\) and \(C=128\) ft.
Substitute these values into the formula: \(s=\frac{45}{360}\times128\).
Simplify \(\frac{45}{360}=\frac{1}{8}\).
Then \(s=\frac{1}{8}\times128\).
Calculate \(\frac{128}{8}=16\).

Answer:

The length of arc \(AB\) is \(16\) ft.