Question

Two satellites are in Earth's orbit and are 424 km apart. If an observer is 658 km away from satellite A and 471 km away from satellite B, what angle must theobserver turn his telescope to change his view from one satellite to another?

Answer 1

Answer:

$O\text{ = 40.0\degree}$

Step-by-step explanation:

If two satellites are in Earth's orbit and are 424 km apart. An observer is 658 km away from satellite A and 471 km away from satellite B. Draw the triangle diagram formed:

To find the angle needed to turn his telescope to change his view from one to another, use the Cosine Law:

$o^2=a^2+b^2-abcos(o)$

Substitute and solve for the angle.

$\begin{gathered} 424^2=471^2+658^2-2(471)(658)cos(O) \\ cos(O)=\frac{221841+432964-179776}{619836} \\ cos(O)=\frac{475,029}{619,832} \\ O=\cos^{-1}(\frac{475029}{619832}) \\ O=39.97\text{ \degree} \\ \text{ Rounding:} \\ O\text{ = 40.0\degree} \end{gathered}$