Question

An arc of length r unit subtends an angle theta at the centre of circle of radius r. find the value of theta

Answer 1

Answer:

Length of Arc, l = 20π cm

Angle subtended by an Arc , θ = 144°

Length of Arc, l = (θ/360) × 2πr

20π = (144°/360°) × 2× π × r

20 = (144°/360°) × 2r

20 = (12/30) × 2r

20 = (⅖)× 2r

20 × 5 = 4r

r = 100/4

r = 25 cm  

Radius of the circle, r = 25 cm

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Answer 2

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• Basically if we observe carefully the length of Arc and the radius both have same length that is "r" units. thus from this we can say that the sector formed is and triangle with all the three sides equal .. thus it is a equilateral triangle l.
• So from this we can say that the value of theta is 60 degress.