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 = ?

Question

please step by step instructions

 

 

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.

Answer 1

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

Answer 2

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

Answer 3

Hi Bella,

The formula for finding the length of an arc is: s = Rθ, where θ is the central angle in radians.

 

 

150^o = (150/180)∏ ≈ 2.62 radians

 

Therefore,

 

s = (2.62)(13.9) ≈ 36.4

 

Hope this helps!

Answer 4

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