Question

Find the length of arc JL. Round to the nearest hundredth.(degrees)

Answer 1

Arc Length

Given a circle of radius r, the length of the arc formed by a central angle θ is given by:

`L=\theta\cdot r`

We are given the central angle ∠JKL = 144° and the radius r = JK = 6 units.

The angle must be converted to radians by using the equivalence π = 180°

Thus:

`\begin{gathered} \theta=144\cdot(\pi)/(180) \\ \theta=2.51327\text{ rad} \end{gathered}`

Calculating the arc length:

`\begin{gathered} L=2.51327\cdot6 \\ L=15.08 \end{gathered}`

The length of the arc JL is 15.08 units