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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 = ?

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.

Belia,

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
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;