s = rθ, where θ is in radians
so, 4*100*pi/180
so, 4*100*pi/180
Arc Length = (θ/360) * 2πr
where:
θ is the angle of rotation in degrees,
r is the radius of the arc's circle.
In this case, θ = 100 degrees and r = 4 feet.
Let's substitute these values into the formula:
Arc Length = (100/360) * 2Ï€(4)
Arc Length = (5/18) * (2Ï€) * 4
Now, let's simplify:
Arc Length = (5/18) * (8Ï€)
Arc Length = (40Ï€/18)
Arc Length ≈ 6.98 feet
Therefore, the length of the arc is approximately 6.98 feet.
The circumference of a circle is calculated using the formula:
C = 2Ï€r
In this case, the radius (r) of the circle is given as 4 feet.
Substituting the value of the radius into the formula, we get:
C = 2Ï€(4) = 8Ï€
We also know that the angle of rotation is 100 degrees.
To find the length of the arc, we need to calculate what fraction of the total circumference is represented by an angle of 100 degrees.
Since a circle has a total angle of 360 degrees, we can set up a proportion to find the fraction of the circumference represented by 100 degrees:
100 degrees / 360 degrees = x / 8Ï€
Simplifying the proportion, we get:
0.2778 = x / 8Ï€
Now, we can solve for x, which represents the length of the arc.
Multiplying both sides of the equation by 8Ï€, we get:
x = 8Ï€ * 0.2778 = 2.219 feet
Therefore, the length of the arc is approximately 2.219 feet.