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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.

An Astronomer Is 450 Light Years 1y From Star A And 400 1y From Star B As Shown Star A Is 90 1yfrom Star BB400 Ly90 LyАAstronomer450 LyIf The Astronomers Telesc class=

Sagot :

Using law of cosines:

[tex]a^2=b^2+c^2-2bc\cos (\alpha)[/tex]

Where:

[tex]\begin{gathered} a=90 \\ b=450 \\ c=400 \\ \end{gathered}[/tex]

So:

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

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