Question

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.

Answer 1

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 arc length. 

⇒ 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.’