Question

Find the arc length of the great circle on a sphere of radius 3000 miles subtended by a central angle of 7°. Express your answer in:
a. Degrees b. Nautical miles

Answer 1

Converting radius from miles to km;

1 mile =1.609km

3000=?

=$3000×1.609km$ =4827km

$r=4827km$

Arch length =$\frac{\theta} {360}2\pi r$

=$\frac{7}{360} ×2× \frac{22}{7}×4827$

=589.97km

b) 1nm=1.852km

?nm =589.97km

=$\frac{1 ×589.97}{1.852}$

=318.5nm