A circle's center is at (7 ,5 )(7,5) and it passes through (5 ,8 )(5,8). What is the length of an arc covering (7pi ) /4 7π4 radians on the circle?
1 Answer
≈ 19.83
Explanation:
To calculate the length of arc , require to know radius of circle.
This can be found using the
color(blue) " distance formula " distance formula
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2d=√(x2−x1)2+(y2−y1)2 where
(x_1,y_1)" and " (x_2,y_2) " are 2 coord points "(x1,y1) and (x2,y2) are 2 coord points The 2 points here are the centre and the point it passes through. This distance is the radius of the circle.
let
(x_1,y_1)=(7,5)" and " (x_2,y_2)=(5,8) (x1,y1)=(7,5) and (x2,y2)=(5,8) hence r
=sqrt((5-7)^2+(8-5)^2)=sqrt(4+9)=sqrt13=√(5−7)2+(8−5)2=√4+9=√13 arc length = circumference
xx " fraction of circle covered "× fraction of circle covered arc length =
2pirxx((7pi)/4)/(2pi) = cancel((2pi)r)xx((7pi)/4)/cancel(2pi) =rxx(7pi)/4
rArr" arc length " = sqrt13xx(7pi)/4 ≈ 19.83
