SOLUTION: Hello! I need help solving this: Use the given arc length and radius to find the angle θ (in radians). The length is 70 and the radius is 56. How much is the angle? I ca

Algebra ->  Trigonometry-basics -> SOLUTION: Hello! I need help solving this: Use the given arc length and radius to find the angle θ (in radians). The length is 70 and the radius is 56. How much is the angle? I ca      Log On


   

Question 978298: Hello!
I need help solving this:
Use the given arc length and radius to find the angle θ (in radians).
The length is 70 and the radius is 56. How much is the angle?
I calculated it once and i got 0.8 but it is not the right answer.
Thank you
Found 2 solutions by rothauserc, Cromlix:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
the radian measure = s / r where s is the length of the arc and r is the length of the radius
radian measure = 70 / 56 = 1.25

Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Full formula is:
Angle/360 = length of arc/Pi x diameter = area of sector/Pi x r^2
................
We will use the first two
Angle/360 = length of arc/Pi x diameter
...
Angle/360 = 70/Pi x 112 (diameter = 2 x r = 2 x 56)
Cross multiply
Angle x Pi x 112 = 70 x 360
Angle = (70 x 360)/(Pi x 112)
Angle = 25200/351.858
Angle = 71.6 degrees.
Hope this helps:-)