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# CAN SOMEONE HELP?

Using the Hubble telescope, scientists discover a new star that is located 52 light years away. Then after rotating the telescope 1.76 degrees to the right they determine another star that is located 35 light years away. Calculate the distance between the two stars. (Note: 1LY = 9.4605284 x 10^12 km).

### 2 Answers

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• Even though this happens in 3-D space, your problem is easy if you treat it as a 2-D triangle (you would then use plane trigonometry).

Draw a flat triangle (on a piece of paper) in this manner.

Pick a point near one corner for Hubble. Call this point "H"

Draw a straight line to a point "N" (for New Star).

Along that line, write the number 52.

At H, you will measure off an angle of 1.76 degrees (one way or the other, it does not matter).  For the drawing, you can exaggerate it - after all, you will use a formula and, as long as you use the correct numbers for the formula, the drawing itself does not have to be extra-precise.

On this new line, put a point "S" located at 35 units from H.

Now join the points N and S to complete the triangle. The question is asking you the length of this "NS" side.

The cosine formula is a tool you can use to find the "opposite side" to a known angle, when you already have the two other sides.

This is what you have:

angle = 1.76 degrees

side HN = 52

side HS = 35

side NS (opposite the known angle at H) is what you want to find.

(NS)^2 = (HN)^2 + (HS)^2 - 2*(HN)(HS)*Cos(H)

(NS)^2 = 52^2 + 35^2 - 2*(52*35)*Cos(1.76 deg.)

(NS)^2 = 2704 + 1225 - 3640*(0.99952828...)

(NS)^2 = 3929 - 3638.2828 = 290.72 (approx.)

All that's left to do is take the square root

• You could use the law of cosines...

C^2 = A^2 + B^2 - 2AB Cos(c), where A and B are the distances given, and the angle c is 1.76 degrees...

C^2 = 52^2 + 35^2 - 2(52)(35) cos(1.76)

C^2 = 2704 + 1225 - (3640(cos(1.76))

C^2 = 3929 - 3638.3

C^2 = 290.7

C = 17.05 ly

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