Hello :) I'm having a problem with this one story problem (Algebra and Trig)

this is supposed to be Law of Sines and Law of Cosines (round to 1 decimal)

Assume that the earth is a sphere of radius 3980 miles. A satellite travels in a circular orbit around the earth, 900 miles above the earth's surface, making one full orbit every 6 hours. If it passes directly over a tracking station at 2 pm, what is the distance from the satellite to the tracking station at 2:05 pm?

I have no clue what to do so I first found the Circumference of the satellite which was 30,661.9miles, I divided that by 6 to find distance in 1 hour which was 5110.3miles, then divided that by 60 to find distance in minutes which was 85.2miles. Multiplied that by 5 to get 425.9miles because the satellite moved 5 minutes over the tracking station. Now I have a triangle say point A to point B is 900miles, point B to C is 425.9miles, what is the length of point C to A?......

WOW typing this out I realized I can just use pythagorean theorem to find the distance. I feel stupid lol. Well if anyone wants to check my answer for me that would be cool :) my answer is 995.7miles. Thanks

Re: Hello :) I'm having a problem with this one story problem (Algebra and Trig)

LOL ok now I am really feeling stupid. I just realized that I cant use Pythagorean Theorem because its not a right triangle. Its formed on a circle so it cant be 90degrees right? I'm just totally confused here how am I supposed to figure this without any angles? if someone could help.

sorry if I'm not supposed to double post... forgot I should just edit original but not sure how to delete this one now.

Re: Hello :) I'm having a problem with this one story problem (Algebra and Trig)

Agree with you up to the distance travelled during the 5 minutes: ~426 miles.

After, you've totally confused me!

You drew a circle circumference 30662 miles (satellite path),

and inside that circle another circumference 25007 miles (Earth),

with common center labelled A ..... OK?

Make the 2 o'clock position point B, the 2:05 position point C:

then arc BC = 426; AB and AC being radius lines.

The supporting angle at A is then 360(426) / 30662 = 5 degrees, right?

Label the inside circle (where Lines AB and AC intersect) at D and E:

length of arc DE is what you're after...unless "they" mean chord DE...

Still with me? I'll leave you the pleasure of wrapping up...