Question

If the measure of GH is 30° and the radius is 6 meters, what is the arc length of GH?

Answer 1

The length of the arc GH is approximately 3.14 meters (or π)

Explanation:

The length of an arc whose measure equals the measure of the central angle Ф and the radius of the circle r is:

• L = (Ф ÷ 360°) × 2π r

Let us solve the question using the rule above

∵ The measure of arc GH is 30°

∴ Ф = 30°

∵ The radius is 6 meters

∴ r = 6 meters

→ Substitute them in the rule above

∵ L = (30° ÷ 360°) × 2π × 6

∴ L =
`(1)/(12)` × 12π

∴ L = π

→ Use π ≈ 3.14

∴ L ≈ 3.14

∴ The length of the arc GH is approximately 3.14 meters (or π)