A circle's center is at (3 ,2 ) and it passes through (5 ,8 ). What is the length of an arc covering (7pi ) /4 radians on the circle?

1 Answer
Aug 14, 2016

Length of the Arc =34.77

Explanation:

Circle's center is at (3,2) and it passes through (5,8)
Therefore Length of the radius=r =Distance between these points(3,2) and (5,8)
or
radius =r=sqrt((5-3)^2+(8-2)^2)
=sqrt(2^2+6^2)
=sqrt(4+36)
=sqrt40
=6.32
Therefore Circumference of the Circle =2pir=2pitimes6.32=39.74
Arc covers (7pi)/4 radians on the Circle
In other words Arc covers (7pi)/4-:2pi=7/8times (circumference of the Circle)
Therefore Length of the Arc =7/8 times2pir=7/8 times39.74=34.77