Question

select the correct answer
arc xy located on circle a has a length of 40 centimeters. the radius of the circle is 10 centimeters. what is the measure of the corresponding central angle for \\(\overset{\frown}{xy}\\) in radians?

a. \\(4\\)

b. \\(3\\)

c. \\(\frac{4}{3}\pi\\)

d. \\(\frac{3}{4}\pi\\)

Explanation:

Step1: Recall arc length formula

The arc length formula relating arc length $s$, radius $r$, and central angle $\theta$ (in radians) is $s = r\theta$.

Step2: Rearrange to solve for $\theta$

Isolate $\theta$ by dividing both sides by $r$: $\theta = \frac{s}{r}$

Step3: Substitute given values

Substitute $s = 40$ cm and $r = 10$ cm:
$\theta = \frac{40}{10}$

Step4: Calculate the value

$\theta = 4$

Answer:

A. 4