a sector of the circle has radius r and angle THETA. find the value of THETA, in radians if the perimeter of the sector equals half the circumference of the circle.
+37084 Perimeter of the circle = 2 pi r
1/2 Perimeter = pi r
Sector circumference portion = theta/(2pi) x 2 pi r = theta r
the sector perimeter ALSO includes two radii lengths r + r
so the total perimeter of the sector = theta r + r + r
and the question states this equals 1/2 perimeter which we found to be pi r....set them equal
theta r + r + r = pi r divide by r
theta + 1 + 1 = pi
theta = pi-2 radians
I hope I did that correctly !
