Answer to Question #136427 in Trigonometry for Jeth palermo

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 miles to kilometres

1 mile = 1.609 km

what about 3000 mile?

= 3000*1.609 = 4827km

arc length=$\theta$ /360 * 2*$\prod$r

=7/360 * 2 * 22/7 * 4827

=589.97km

b. 1nm=1.852km

then how many nm will make 589.97km

=(1*589.97)/1.852km

=318.5nm