Question

In the circle E, angle CED=145 and the length of CE is 12 cm. what is the length of arc CD

Answer 1

Given:

a.) Angle CED = 145°

b.) Length of CE is 12 cm.

To be able to get the arc length of CD, we will be using the following formula:

`\text{ Arc Length = 2}\pi r\text{ (}(\theta)/(360^(\circ)))`

Where,

r = radius of the circle

θ = angle

We get,

`\begin{gathered} \text{ Arc Length = 2}\pi r\text{ (}(\theta)/(360^(\circ))) \\ \text{ = 2}\pi(12)((145^(\circ))/(360^(\circ))) \\ \text{ = 24}\pi((29)/(72)) \\ \text{ = }(696\pi)/(72) \\ \text{ = 30.35333}\ldots\text{ }\approx\text{ 30.35 cm.} \end{gathered}`

Therefore, the length of arc CD is 30.35 cm.