an arc of a circle subtends a central angle of 5pi/6 radians.if the radius of the circle measures 10.6cm, determine the approx measure of the arc leanth

To determine the approx measure of the arc length, you can use the formula:

Arc Length = (central angle / 2π) * (2π * radius)

Given:
Central angle = 5π/6 radians
Radius = 10.6 cm

Substituting the values into the formula, the equation becomes:

Arc Length = (5π/6 / 2π) * (2π * 10.6)

Simplifying:

Arc Length = (5π/6) * 10.6

Now, let's calculate the approximation using 3.14 as an approximate value for π:

Arc Length ≈ (5 * 3.14 / 6) * 10.6

Arc Length ≈ (15.7 / 6) * 10.6

Arc Length ≈ 2.617 * 10.6

Finally, calculating the approximate arc length:

Arc Length ≈ 27.7492 cm

Therefore, the approximate measure of the arc length is approximately 27.7492 cm.

To determine the approximate measure of the arc length, you need to know the formula for finding the arc length of a circle. The formula is as follows:

Arc Length = (Central Angle / 2π) × (2π × radius)

In this case, the given central angle is 5π/6 radians, and the radius of the circle is 10.6 cm. Plugging these values into the formula, you get:

Arc Length = (5π/6 / 2π) × (2π × 10.6)

First, simplify the fraction by canceling out the common factors of π:

Arc Length = (5/6 / 2) × (2π × 10.6)

Now, simplify the fraction:

Arc Length = (5/6) × (2π × 10.6)

Next, multiply 2π and 10.6:

Arc Length = (5/6) × (21.2π)

Finally, calculate the approximate value using a calculator.

Arc Length ≈ 17.65 cm

Therefore, the approximate measure of the arc length is 17.65 cm.

s = rθ = 10.6 * 5π/6 = 27.75 cm