The arc length traveled by the needle is 7.0904
Step-by-step explanation:
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<u>Step 1</u>
In the above question are given that
The speedometer needle in a car is 2.5 inches long
The needle sweeps out an arc of 130°.
Let r be the length of the speedometer needle,So
r=2.5
m∠C=130°
<u>Step 2</u>
The formula for determining the area of the sector is
A=
*
Where,the central angle is m°
and The radius is r
Substituting the value of m and r from the step 1 in the below equation we get
A=
*
A= 0.3611*
*6.5=7.0904 
Hence the value of the Area of the sector is = 7.0904 
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<u>Step 3</u>
<u>So, the arc length traveled by the needle </u><u> 7.0904 </u>
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