A minor arc of a circle subtends an angle of 105 degree at the center of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc. 22/7
oops. that is the minor arc.
Change 105 to (360-105)
that would of course be
s = rθ = 8.4 * 105(π/180)
Answer
To find the length of the major arc, you need to use the formula:
Length of arc = (angle/360) * 2π * radius,
where angle is the measure of the central angle in degrees, radius is the radius of the circle, and π is a constant approximately equal to 3.14 or 22/7.
In this case, the angle is given as 105 degrees, and the radius is given as 8.4 cm. So, substituting these values into the formula:
Length of arc = (105/360) * 2π * 8.4,
Now, simplify and calculate:
Length of arc = (105/360) * (2 * (22/7)) * 8.4,
Length of arc = (3/8) * (22/7) * 8.4,
Length of arc = 3 * 22 * 1.2,
Length of arc = 79.2 cm.
So, the length of the major arc is 79.2 cm.