Use the Law of Sines to answer the following question The pa

Use the Law of Sines to answer the following question.

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 49 km apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.5 degree and 85.1 degree, respectively.

Solution

Let the postion ( vertex) of satelleite be denoted as C in triangle

Now the interior angle A in triangle would be = 180 -87.5 = 92.5 deg

The thidr angle of triangle = 180 - 92.5 - 85.1 = 2.4 deg

AB = 49 km

Applying sine rule in triangle to find distance from satellite AC/sin85.1 = 49/sin2.4

AC = 1165.85 ( Distance from station A)

To find height drop a perpendicualr from on AB: Perpendicular(h) is the height of satellite

Now in the right angled triangle with h and AC and acute angle = 87.5 deg .Apply trigonometric ratio:

h/AC = sin87.5

h = 1164.74 km ( Height of satellite)