Trigonometry
posted by Mercaedees .
FInd the arc length intercepted by a central angle of 46 degrees 24'6" in a circle with a radius of 35.62m

The total circumference of the circle is 2 pi R = 2 pi *35.62 = 223.8 meters
I kept five significant figures because the original radius had five.
Now how much of that circumference are we interested in?
fraction = 46 deg 24 min 6 sec / 360 degrees
we need to put that all in degrees
46 + 24/60 + 6/3600 = 46+.4+.0017
= 46.40 degrees out of total 360
so
we have
(46.40/360)223.8 = 28.85 meters 
Typo  I kept four significant figures because the original radius had four.