SOLUTION: In the following problem, θ is a central angle that cuts off an arc of length s. Find the radius of the circle. (Round your answer to two decimal places.) θ = 150°, s =

Algebra ->  Triangles -> SOLUTION: In the following problem, θ is a central angle that cuts off an arc of length s. Find the radius of the circle. (Round your answer to two decimal places.) θ = 150°, s =       Log On


   

Question 1128109: In the following problem, θ is a central angle that cuts off an arc of length s. Find the radius of the circle. (Round your answer to two decimal places.)
θ = 150°, s = 5 km


km = ?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

First,  S = r%2Atheta :  the arc length is the radius times the central angle measure in radians.


Second,  150 degrees = %285%2F6%29pi radian.


Therefore,  R = S%2Ftheta = 5%2F%28%285%2F6%29pi%29 = %285%2A6%29%2F%285%2Api%29 = 6%2Fpi = 6%2F3.14 = 1.91 kilometer.   ANSWER

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+150%2F360+=+5%2FC+
+5%2F12+=+5%2FC+
The circumference, C is +12+ km
+C+=+2pi%2Ar+
+12+=+2%2Api%2Ar+
+r+=+6%2Fpi+
+r+=+1.91+ km