A Global Positioning System satellite orbits a 11500 miles

A Global Positioning System satellite orbits a\' = 11,500 miles above Earth\'s Surface (see figure), Find the angle of depression from satellite to the radius of Earth is 4000 miles. (Round your answer to two decimal places.)

Solution

let the angle of depression be

Global positioning of saletellite is 11500 miles above surface of earth

==> it\'s distance from centre of earth = (d + 4000) = (11500 + 4000)

==> 15500 miles

from figure sin(90 - ) = 4000/(d + 4000)

==> cos = 4000/15500

==> cos = 8/31

==> = cos^-1 (8/31)

==> = 75.04^o

Hence angle of depression = 75.04^o