Question

Find the distance along an ark on the surface of the earth that subtends a central angle of 10 minutes (1 minutes 1/60 degree) The radius of the earth is 3960 miles around to the thousands

Answer 1

11.52 miles

Explanation:

We know that the length of an arc L = Ф/360 × 2πR where Ф = angle subtended by arc and R = radius of circle.

Now since Ф = 10 minutes = 10 × 1 minute = 10 × (1/60)° = (1/6)° and R = radius of earth = 3960 miles

So L = Ф/360 × 2πR

= (1/6)°/360 × 2π(3960 miles)

= 1/2160 × 7920π

= 3.67π

= 11.52 miles