A wire of length 121 cm is bent so as to lie along the arc of a circle of radius 180 cm. Find in degrees; the angle subtended at the centre by the arc.
θ will be in degrees.
Arc-length can be given by the formula : θ / 360° × 2πr
Hence it is given that 121 cm is the arclength.
⇒ 121 = θ / 360° × 2πr
= 121 = θ / 360° × 2 × 22 / 7 × 180
= 121 = θ / 360° × 360 × 22 / 7
= 121 = θ × 22 / 7
⇒ θ = 121 × 7 / 22
= 38.5°
Hence the angle subtended at the middle is 38.5°
Which can also be written as 38° 30.’