Finding arc length

Question

the radius of the earth is 3960 miles. the distance along an arc on the surface of the earth that subtends a central angle of 1 minute (minute=1/60 degree)

Answer 1

s = 2πrθ / 360

s = 2π(3960)(1/60) / 360

s = 2π / 21600

s = 7920π / 21600

s = 1.151917306

Answer 2

Hi, Chloe!

The key to this problem is to use the arc length formula: s = rθ, where s is the arc length, r is the radius, and θ is the angle measurement (in radians).

We are given r = 3,960 miles and θ = 1/60 degrees.

Before we plug these values into the equation, we need to convert the angle into radians. In order to do so, we can multiply our angle by (π/180):

θ = (1/60) × (π/180)

θ ≈ 2.9 × 10^-4 radians

Now we can directly plug this into our formula for arc length

s = rθ

s = (3960)(2.9 × 10^-4)

s ≈ 1.1484 miles

(You can round this to whatever place your teacher expects; also, be sure to include the units of miles in your answer!)

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!