in a circle of radius 7m, find the length of the arc subtended by a central angle of 42.0degrees
2πR*(42/360)
R=radius
circumference = 14π
so
arc/14π = 42/360
arc = 14π(42/360) = appr 5.13 m
Thank you both!
To find the length of the arc subtended by a central angle in a circle, you can use the formula:
Arc Length = (θ/360) * (2πr)
Where:
Arc Length is the length of the arc.
θ (theta) is the central angle in degrees.
r is the radius of the circle.
In this case, the radius of the circle is given as 7m and the central angle is given as 42.0 degrees. Let's plug in these values into the formula:
Arc Length = (42.0/360) * (2 * 3.14159 * 7)
First, calculate the value in parentheses:
(42.0 degrees / 360 degrees) = 0.1167 (rounded to four decimal places)
Now, calculate the value outside the parentheses:
(0.1167) * (2 * 3.14159 * 7) = 12.0874 meters (rounded to four decimal places)
Therefore, the length of the arc subtended by a central angle of 42.0 degrees in a circle with a radius of 7m is approximately 12.0874 meters.