The length of an arc of a circle is 12cm. The corresponding sector area is 108cm2.
Find:
+128407
Arc length, S, = r * θ wher r is the radius and θ is in radians
Area of a sector = (1/2) (r^2)*θ
So........
12 = r * θ → θ = 12 / r (1)
And
108 = (1/2) (r^2) * θ subbing (1) into this, we have that
108 = (1/2) (r^2) * (12 /r) simplify
216 = 12 r divide both sides by 12
18 = r = the radius
And to find the angle subtended by the arc is given by θ = 12 / r → θ = 12 / 18 = 2 / 3
And this is in rads......so to convert to degrees we have ..... (2/3) * 180° / pi ≈ 38.19°
