# Trigonometry

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

• Trigonometry -

The total circumference of the circle is 2 pi R = 2 pi *35.62 = 223.8 meters
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

• Trigonometry -

Typo - I kept four significant figures because the original radius had four.

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