Find the length s of the arc that subtends a central angle o

Find the length s of the arc that subtends a central angle of measure 20 degree in a circle of radius 16 m. () s = ________________ m A central angle theta in a circle of radius 6 m is subtended by an arc of length 7 m. Find the measure of theta in degrees. () theta = _______________ degree Find the measure of theta in radians. () theta = ________________ rad

Solution

Answer 15.

The formula of length of an arc is s = r where is in radians.

Radius r is given as 16 m.

is given as 20 deg. Converting 20 degree into radian , will become 20 * pi/180 = 0.34906585 radians

So, putting the value in formula

s = r = 16 * 0.34906585 = 5.5850536

s = 5.59 m

Answer 16.

The formula for angle = = s/r

= 7/6 = 1.1666 = 1.17 radians

In degrees, 1.1666* 180/pi = 66.8450 = 66.8 degrees

Hence answer a would be 66.8 degree and answer b is 1.17 radians.