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.
To find the arc length, you can use the formula:
Arc Length = (Central Angle / 360°) * 2π * Radius
Given:
Central Angle = 46 degrees 24'6"
Radius = 35.62m
First, convert the angle to decimal degrees:
46° + (24/60)° + (6/3600)° = 46.41°
Now, we can substitute the values into the formula to find the arc length:
Arc Length = (46.41° / 360°) * 2π * 35.62m
To find the arc length intercepted by a central angle, we can use the formula:
Arc Length = (Central Angle / 360) * 2 * π * Radius
Now let's plug in the values:
Central Angle = 46 degrees 24'6" = 46 + 24/60 + 6/3600 degrees
Radius = 35.62 m
First, we need to convert the central angle from degrees, minutes, and seconds to decimal degrees.
To convert minutes to degrees, divide by 60: 24/60 = 0.4 degrees
To convert seconds to degrees, divide by 3600: 6/3600 = 0.00167 degrees
So, the central angle in decimal degrees is:
46 + 0.4 + 0.00167 = 46.40167 degrees
Now we can calculate the arc length:
Arc Length = (46.40167 / 360) * 2 * π * 35.62
Simplifying this equation will give us the final answer.