Respuesta :
Answer: 2.62 unit (approx)
Step-by-step 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°
[tex]\text{Since } 180^{\circ} = \pi \text{ radian}[/tex]
[tex]\implies 1^{\circ} = \frac{\pi}{180}\text{ radian}[/tex]
[tex]\implies 75^{\circ} = \frac{75\pi}{180}\text{ radian}= \frac{5\pi}{12}\text{ radian}[/tex]
[tex]\implies \text{ The central angle of the given arc} = \frac{5\pi}{12}\text{ radian}[/tex]
[tex]\text{ Thus, } \text{The length of the given arc} = 2 \times \frac{5\pi}{12}[/tex]
[tex]= \frac{5\pi}{6}[/tex]
[tex]= 2.61799388\text{ unit}\approx 2.62\text{ unit}[/tex]
