Find the length of the arc (sector question)
Radius=8cm
Angle=27
arc length = rØ where Ø is in radians
I assume your angle of 27 is 27°
27° = (27/180)π radians = (3/20)π radians
arc length = 8(3/20)π cm
= 6π/5 cm
To find the length of an arc, you can use the formula:
Arc Length = (angle / 360) * (2 * π * radius)
In this case, the radius is given as 8 cm and the angle is given as 27 degrees.
First, convert the angle from degrees to radians by using the formula:
radians = (degrees * π) / 180
So, for an angle of 27 degrees,
radians = (27 * π) / 180
Next, substitute the values into the arc length formula:
Arc Length = (radians / 360) * (2 * π * radius)
Arc Length = ((27 * π) / 180) / 360) * (2 * π * 8)
Simplify the expression:
Arc Length = (27π / 180) * (2π * 8) / 360
Arc Length = (27π / 180) * (16π / 360)
Arc Length = (27 * 16 * π^2) / (180 * 360)
Finally, calculate the arc length:
Arc Length ≈ 4.24 cm