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June 27th, 2013, 06:43 AM   #1
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trigonometry in earth

Can someone help me? Suppose the earth to be a real sphere with the radius R. The arc distance from HK (N23) to the North pole is:
a)2.2R
b)1.2R
c)0.9R
How to solve it? I really need the work ASAP if it does not burden you.

Last edited by skipjack; June 13th, 2017 at 05:01 AM.
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June 27th, 2013, 07:18 AM   #2
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Re: trigonometry in earth

Total circumference of the earth = $2\pi \text{R}$
arc length we need is with an angle of 90° - 23° = 67°
so the arc distance is $\displaystyle \frac {67}{360}*2\pi \text{R} =1.17\text{R}$, so I guess answer b is right.

Last edited by skipjack; June 13th, 2017 at 04:52 AM.
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June 13th, 2017, 05:08 AM   #3
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Although HK has a latitude of 22.3964° North, which by the same method leads to $1.18\text{R}$, I have to agree with the above post.
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June 15th, 2017, 06:22 AM   #4
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"HK" is, of course, "Hong Kong".
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