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.
+129838 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.
The perimeter of the sector = 2r + rθ = r (2 + θ )
The circumference of half of the circle = pi * r
So we have that
r (2 + θ ) = pi * r divide both sides by r
2 + θ = pi subtract 2 from both sides
θ = [ pi - 2 ] rads ≈ 65.4°
