Question

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {5 \pi / 8} & {2} & {? }\end{array}\)

Short answer

The arc length \(s\) is \( \pi 5/4 units\).

Step-by-step solution

Identify Given Information

The angle \(\theta\)= \(5 \pi / 8\) rad and the radius \(r\)=2.

Apply the Arc Length Formula

The arc length \(s\) can be found by using the formula: \(s = r \times \theta\). Hence, substituting the values: \(s = 2 \times (5 \pi / 8) \).

Simplify Expression

Calculate the multiplication: \(s= \pi 5/4\). This will give the length of arc subtended by the given angle at the center of the circle.