a segment of late 94 cm has been rotated d degrees around a center zero what is the length of the rotated segment
rotation does not change lengths.
To find the length of the rotated segment, we need to know the angle of rotation (d) and the length of the original segment (94 cm).
The formula to calculate the length of the rotated segment is:
Length of rotated segment = θ/360 * 2π * r
where θ is the angle of rotation and r is the radius of the circle.
Since we know the length of the original segment (94 cm), we need to find the radius of the circle.
The formula to find the radius of the circle is:
r = original segment length / (2π)
Substituting the given value:
r = 94 cm / (2π)
Now, we can calculate the length of the rotated segment:
Length of rotated segment = d/360 * 2π * r
Substituting the values we found:
Length of rotated segment = d/360 * 2π * (94 cm / (2π))
Simplifying:
Length of rotated segment = d * 94 cm / 360
Therefore, the length of the rotated segment is given by d * 94 cm / 360, where d is the angle of rotation.
To determine the length of the rotated segment, we need to apply the formula for the arc length of a circle.
The formula for the arc length is given by:
Arc Length = (θ/360) * (2 * π * r),
where θ is the central angle in degrees, and r is the radius of the circle.
In this case, the central angle is given as "d" degrees, and the radius is half the length of the segment, which is 94 cm / 2 = 47 cm.
Substituting the given values into the formula, we get:
Arc Length = (d/360) * (2 * π * 47).
Now we can solve for the length of the rotated segment.