If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.
Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.
From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.
Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.
So,
length of arc LNM=Circumference of circle-length of arc LKM.
We know that length of an arc =Θr
in which Θ is the angle in radian.
length of arc=70*π[tex]/180*5[/tex]
=70π[tex]/36[/tex]
Circumference of circle=2π*5
=10π
Length of arc LNM=10π-70π[tex]/36[/tex]
=(360π-70π)[tex]/36[/tex]
=290π[tex]/36[/tex]
Put π=3.14
=290*3.14[tex]/36[/tex]
=910.6[tex]/36[/tex]
=25.29m
Hence the length of arc LNM is 25.29 m.
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