Question

Given a circle with a radius of 2 which is the length of an arc measuring 75

Answer 1

Answer: 2.62 unit (approx)

Explanation:

Since, the length of an arc of a circle = Radius × Central angle by the arc on the circle( In radian )

Here the radius = 2 unit

And, the central angle by the arc on the circle = 75°

`\text{Since } 180^(\circ) = \pi \text{ radian}`

`\implies 1^(\circ) = (\pi)/(180)\text{ radian}`

`\implies 75^(\circ) = (75\pi)/(180)\text{ radian}= (5\pi)/(12)\text{ radian}`

`\implies \text{ The central angle of the given arc} = (5\pi)/(12)\text{ radian}`

`\text{ Thus, } \text{The length of the given arc} = 2 * (5\pi)/(12)`

`= (5\pi)/(6)`

`= 2.61799388\text{ unit}\approx 2.62\text{ unit}`