Question

find the distance along an arc on the surface of the earth that subtends a central angle of 10 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles.

Answer 1

The length of the arc = 11.52 miles

Step-by-step explanation

The length of an arc is given as

`\text{Length of an arc = }(\theta)/(360\degree)*2\pi r`

For this question,

θ = Angle subtended at the middle of the circle we are concerned about = 10 minute = (10/60) degrees = 0.167 degrees

π = pi = 3.142

r = radius of the earth = 3960 miles

`\begin{gathered} \text{Length of an arc = }(\theta)/(360\degree)*2\pi r \\ \text{Length of an arc = }(0.167\degree)/(360\degree)*2\pi*3960 \\ =11.52\text{ miles} \end{gathered}`

Hope this Helps!!!