find the arc length of the minor arc withe degree of 120 and a radius of 8
whole circumference = 2π(8) = 16π
arc/16π = 120/360
arc / 16π = 1/3
arc = 16π/3
To find the arc length of a minor arc, we can use the formula:
Arc Length = (θ/360) * 2π * r
Where:
θ is the degree measure of the arc.
r is the radius of the circle.
In this case, the degree measure of the arc is 120 degrees, and the radius is 8.
Plugging these values into the formula:
Arc Length = (120/360) * 2π * 8
First, simplify the fraction:
Arc Length = (1/3) * 2π * 8
Now, calculate the value of 2π:
Arc Length = (1/3) * 2 * 3.14 * 8
Multiply the values:
Arc Length = (1/3) * 6.28 * 8
Simplify and calculate:
Arc Length = 2.09 * 8
Arc Length = 16.72
Therefore, the arc length of the minor arc with a degree of 120 and a radius of 8 is approximately 16.72 units.
To find the arc length of a minor arc, you can use the formula:
Arc Length = (θ / 360) × 2πr
Where:
θ = angle in degrees
r = radius of the circle
In this case, the angle is 120 degrees and the radius is 8. Plugging these values into the formula, we get:
Arc Length = (120 / 360) × 2π × 8
Simplifying this, we have:
Arc Length = (1/3) × 2π × 8
Next, calculate the values inside the parentheses:
Arc Length = (1/3) × 2 × 3.14159 × 8
Arc Length = (1/3) × 6.28318 × 8
Finally, solve the multiplication and division to find the arc length:
Arc Length ≈ 16.7553
Therefore, the arc length of the minor arc with a degree of 120 and a radius of 8 is approximately 16.7553 units.