Respuesta :
The length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.
What is the length of the arc of a circle?
The length of the arc of a circle is equal to the product of the circumference of the circle and the ratio of the angle made by the arc of the circle to 2π. It is given by the formula,
[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]
It is given that the radius of the circle is equal to 2 ft while the angle made by the arc at the centre of the circle is equal to [tex]\dfrac{5\pi}{3}[/tex]. And we know the formula for the length of the arc, therefore, the length of the arc,
[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]
[tex]= 2\pi \times 2 \times \dfrac{\frac{5\pi}{3}}{2\pi}\\\\= 10.471 \approx 10.5\rm\ ft[/tex]
Hence, the length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.
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