If the perimeter of the sector shown in the figure is 18, with radius 4. What is the angle of the sector in radians?
+23246 The perimeter of the sector consists of the two radii and the arc.
The two radii (together) have a length of 8.
This leaves 18 - 8 = 10 for the length of the arc.
Now, we need to find the circumference of the circle: C = 2·pi·r = 2·pi·4 = 25.1327 (approximately).
Radians / 2pi = arc length / circumference
Radians / 2pi = 10 / 25.1327 = 0.3979 (approximately)
Radians = 0.3979 x 2pi = 0.796pi = 2.5 (approximately)
