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

`O\text{ = 40.0\degree}`

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)=(221841+432964-179776)/(619836) \\ cos(O)=(475,029)/(619,832) \\ O=\cos^(-1)((475029)/(619832)) \\ O=39.97\text{ \degree} \\ \text{ Rounding:} \\ O\text{ = 40.0\degree} \end{gathered}`