The length of the arc is 15.70 km
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
The formula is given by
s = ϴ × r,
where
s is the arc length
r is the radius of the circle
θ is the central angle of the arc in radians
Given :- Radius = 10km
Angle = 90 ° = [tex]\pi[/tex]/2 radians (1 radian = 180°/[tex]\pi[/tex])
By using formula we get
Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km ([tex]\pi[/tex] = 3.14)
= 15.70 km
Thus the length of the arc is 15.70 km
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