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5.If s denotes the length of the arc of a circle of radius r subtended by a central angle ?, find the missing quantity.r = 13.9 inches, ? = 150°, s = ?

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If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.r = 13.9 inches, θ = 150°, s = ?
 
 
A) 36.6 in.B) 36.7 in.C) 36.5 in.D) 36.4 in.
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4 Answers

Belia,
Let's start by thinking about what we know about a circle.
 
1) Circumference C = 2(Pi)D  
2) Total Angle in a circle is 360 degrees
 
Since they gave you theta, just figure out what fraction of the total angle of the circle this is:   150/360 = .4167
 
Then calculate the Total Circumference of the Circle = 2(3.14)(13.9) = 87.3
 
So the arc length is (.4167) * (87.3) = 36.38  which rounds to 36.4
 
Does that make sense? If not post a follow-up comment and we'll go from there.
 
Paul
Circumference of circle:
 
C = (pi)*D = 2*(pi)*r = 2*(pi)*13.9 inches = 87.336 onches
 
(150°)/(360°) = 5/12
 
∴s = (5/12)*(87.336 inches) = 36.39 inches
Hi Bella,

The formula for finding the length of an arc is: s = Rθ, where θ is the central angle in radians.
 
 
150o = (150/180)∏ ≈ 2.62 radians
 
Therefore,
 
s = (2.62)(13.9) ≈ 36.4
 
Hope this helps!
The length of an arc is simply l=r*θ*π/180, where θ is in degrees, π≈3.1415926
 
To understand where this formula came from, recall that the total circumference of a circle is 2πr. The complete circle is 360 degrees, so the arc subtended by 1 degree central angle is simply 2πr/360 or πr/180. Then if the central angle is θ degrees, the arc length is:
l=πr/180*θ;
 
In your case, l≈3.14*13.9*150/180=3.14*13.9*5/6≈36.4 in. 
 
Answer: D

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