Respuesta :

Answer:

[tex]m(RS)=17[/tex] inches  (answer rounded to nearest tenths)

Step-by-step explanation:

Central angle there is 150 degrees.

The radius is 6.48 inches.

The formula for finding the arc length, RS, is

[tex]m(RS)=\theta \cdot r[/tex]

where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.

I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].

[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]

[tex]m(RS)=16.96[/tex] inches

luisejr77

Answer: [tex]17\ in[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Arc Lenght:

[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]

Where "r" is the radius and  "C" is the central angle of the arc in degrees.

You can identify in the figure that:

[tex]r=6.48\ in\\C=150\°[/tex]

Then, you can substitute values into the formula:

[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]

Rounded to the nearest tenth, you get:

[tex]Arc\ RS=17\ in[/tex]  

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