Question

Find the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles.

Answer 1

The distance is 6.9115 miles.

Explanation:

To solve this problem we can use a rule of three.

The length of a circumference is 2*pi*r, and if we have a fraction of the whole arc, we have that:

360 degrees -> arc of 2*pi*r

6 * (1/60) degrees -> arc of x

So we have that:

`x * 360 = (1/10) * 2*\pi*r`

`x = (1/10) * 2 * \pi * 3960 / 360`

`x = (1/5) * \pi * 11`

`x = (11/5)*\pi = 6.9115\ miles`

The distance is 6.9115 miles.