How do i solve this? Find the radius of a circle that has an arc length of 7 feet that subtends an angle of 110 degrees. b) find the area of the sector of the circle described above.

So I converted 110 degrees to radian and got 11/18Pi is the radius 35.98 or is it 3.64. i'm getting confused i guess where the pi is placed to caluclate.

1 Answer
May 13, 2018

r=3.64609506 feet

Area of sector = 12.76133271 #feet^2#

Explanation:

Why change to radians?
#C=piD#
Arc length is #(theta)/360piD#

#110/360 piD=7#

#D=(7xx36)/(11pi)#

#r=(7xx18)/(11pi)#

#r=126/(11pi)#

Area#=110/360 xx pi xx (126/(11pi))^2#

Area of sector = 12.76133271 #feet^2#