1.2 Arc Length & Area of The Circle
O is the centre of the circle of radius 'r' (r
> 0) . A central angle of qc
radians intercepts an arc AB of length 's'. We know that angle subtended
at the centre (is proportional to the ) length of the arc.
= K . s .....(1)
where K is a constant.
Let `C' be any point on this circle such that Ð
BOC = 1 radian so that length of arc BC = r
\ 1c = K . r .....(2)
Comparing the two relations (1) and (2) we have =
Note : In this formula q is
always in radians with r and s are measured in the same units of
But when qis measured in degrees,
For military purpose this written as W = Rm where
m is the central angle in mils. R is the radius (range) expressed
in thousands of meters and W is the chord (width) expressed in meters.