SOLUTION: A central angle of 140� subtends an arc of length 10 feet on a circle. Find the radius of the circle Please explain Thank you

Click here to see ALL problems on Trigonometry-basics

Question 968360: A central angle of 140� subtends an arc of length 10 feet on a circle. Find the radius of the circle
Please explain
Thank you
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A central angle of 140� subtends an arc of length 10 feet on a circle. Find the radius of the circle
--------
140 degrees = 140(pi/180) = (7/9)pi radians
------
Equation:
theta in radians = (arc length)/(radius)
(7/9)pi = 10/radius
---
radius = 10/[(7/9)pi] = 90/(7pi) is approximately 4.09 ft
-------------------
Another way to work it using proportions::
circum/360 = arc/central angle
cir/360 = 10/140
cir = 3600/140 = 25.71
---
2*pi*r = 25.71
radius = 25.71/(2*pi) = 4.09 ft.
------
Cheers,
Stan H.
-------------