Chapter 4.8, Problem 27E

To determine

To find: the angle of depression from the satellite to horizon.

Answer to Problem 27E

The angle of depression from the satellite to the horizon is $\theta =75.97°$ .

Explanation of Solution

Given information:

A global positioning system satellite orbits 12500 miles above Earth’s surface. Assume the radius of Earth is 4000 miles.

  Calculation:

Assume that a Global Positioning system satellite orbits 12500 miles above Earth’s surface.

  

Since the sine of the angle is given by the ratio of the length of the perpendicular to the hypotenuse, therefore in $\Delta OAB$

  $\sin B=\frac{OA}{OB}$

Put the values

  $\begin{array}{l}\sin B=\frac{4000}{12500+4000}\\ \sin B=\frac{4000}{16500}\end{array}$

Thus

  $\begin{array}{c}B={\sin }^{-1}\left(\frac{4000}{16500}\right)\\ ={\sin }^{-1}\left(0.2424\right)\\ =14.03°\end{array}$

Therefore, the angle of depression is

  $\begin{array}{c}\theta =90°-14.03°\\ =75.97°\end{array}$

Thus, the angle of depression from the satellite to the horizon is $\theta =75.97°$ .