Question

If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

Answer 1

radius `r=11 yards`.

Explanation:

First convert the radians into degrees.
`1 rad=(180/pi)degrees`
`0.5 rad=0.5*(180/pi)degrees=(90/pi)degrees`
`theta/360*2pir=`length of an arc, where, `theta` is the angle subtended by the arc in degrees.
Thus, plugging in the values in the equation,
we get:
`(90/pi)*1/360*2*pi*r=5.5` yards
Simplify that to get:
`(r/2)=5.5` yards
`r=5.5*2` yards
`=11 yards`

Hope that helps!!