Question

An astronomer is 450 light years (1.y.) from star A and 400 1.y. from star B, as shown. Star A is 90 1.y.from star B.B400 l.y.90 l.y.АAstronomer450 l.y.If the astronomer's telescope is currently pointed at star A, how many degrees must she rotate hertelescope to see star B?Do not round during your calculations. Round your final answer to the nearest degree.

Answer 1

Using law of cosines:

`a^2=b^2+c^2-2bc\cos (\alpha)`

Where:

`\begin{gathered} a=90 \\ b=450 \\ c=400 \\ \end{gathered}`

So:

`\begin{gathered} \cos (\alpha)=(450^2+400^2-90^2)/(2\cdot400\cdot450) \\ \cos (\alpha)=(354400)/(360000) \\ \alpha=\cos ^(-1)((59)/(60)) \\ \alpha\approx10^(\circ) \end{gathered}`