Question

The speedometer needle in a car is 2.5 inches long. When accelerating from 0 to 60 miles per hour the needle
sweeps out an arc of 130°. What is the arc length traveled by the needle? Round your answer to the nearest
hundredth.

Answer 1

The arc length traveled by the needle is 7.0904$in^{2}$

Step-by-step explanation:

Step 1

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°

Step 2

The formula for determining the area of the sector is

A=$\frac{m}{360}$*$\pi r^{2}$

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=$\frac{130}{360}$*$\pi *2.5^{2}$

A= 0.3611*$\pi$*6.5=7.0904 $in^{2}$

Hence the value of the Area of the sector is = 7.0904 $in^{2}$

Step 3

So, the arc length traveled by the needle 7.0904 $in^{2}$