Question

Complete the table.

Distance, s (Arc length)
? yd
Radius, r
4.4 yd
Angle, 0
7T
4
Distance, s (Arc length)
yd
4.4 yd
4
(Do not round until the final answer. Then round to the nearest hundredth
as needed.)
Radius, r
Angle, 0
7T

Answer 1

The arc length
`(\(s\))` of a circle with a radius of 4.4 yards and an angle of
`\(7\pi/4\)` radians is approximately 24.19 yards, calculated using the formula
`\(s = r \cdot \theta\).`

I assume you want to calculate the arc length based on the given radius and angle. The formula for arc length (s) is given by:

`\[ s = r \cdot \theta \]`

where:

-
`\( s \)` is the arc length,

-
`\( r \)` is the radius, and

-
`\( \theta \)` is the angle in radians.

If you have the angle in degrees, you need to convert it to radians using the conversion factor
`\( (\pi)/(180) \).`

Let's use the formula to calculate the arc length:

Given:

- Radius,
`\( r = 4.4 \) yd`

- Angle,
`\( \theta = 7\pi/4 \)` radians

`\[ s = 4.4 \cdot (7\pi)/(4) \]`

Now, let's calculate it:

`\[ s \approx 4.4 \cdot (7 \cdot 3.14159)/(4) \]`

`\[ s \approx 4.4 \cdot (21.99113)/(4) \]`

`\[ s \approx 4.4 \cdot 5.49778 \]`

`\[ s \approx 24.190792 \, \text{yd} \]`

So, the arc length
`(\( s \))` is approximately
`\( 24.19 \)` yards.