Basic geometry help

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Making a post for @nimble tapir since they apparently don't know how to use the help channels for their benefit 👍

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Here's the full pic

Why yes Kamisato, I might be able to help with this problem! Thank you kindly for opening a help channel rather than DMing some random user :)

Alright we know XSY is 140. Since line segment XY is perfectly vertical and intersects points X and Y (which form a triangle with point O), this means angles SXN and SYN must be equal

Since XSY forms a triangle and we are given angle S is 140, this means that 140 + 2x (where x = angle SXN) must equal 180. Hence x = 20. Since angle SXO is a right angle, this means that angle NXO must be 70 degrees

But since XNO forms a right triangle, we have angle XNO = 90. Then, we must have XNO + NXO + XON = 180, which means 90 + 70 + XON = 180, and hence we have angle XON = 20 degrees

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Now from here we also get that angle SYN is 20 degrees and hence NYO is 70 degrees and then we do the next step to get that YON is 20 degrees

Hence XOY is 20 + 20 = 40

Now for 6c

We found that angle XON was 20 degrees earlier

Now since we see that cos(XON) = (ON)/r, we have that ON = r*cos(XON)

We are given r as 6372 km and know XON = 20 degrees

So ON = 6372 km * cos(20 deg) = 5987.72 km

Hope that helps my friend!

Once again, thank you for not harassing some random to do your homework for you and instead asking in the help channels 👍