Use the arc length formula and the given information to find θ. s = 4 m, r = 13 m; θ = ?

C=2πr and the circumference is measured at 360°

So if we were to set up a proportion we could say:

s/(2πr)=α/360

α=180s/(πr)

We are given that s=4m and r=13m so:

α=180(4)/(13π)

α=720/(13π) m  which is approximately:

α≈17.63°

Which is why radians are often used, because in radians...

α=[720/(13π)](π/180)

α=4/13 rads

Or the arc length in radians is simply expressed as:

s=rα

α=s/r  (which is much neater :P) then it is plain to see that:

α=4/13  rads