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 June 27th, 2013, 05:43 AM #1 Member   Joined: Dec 2011 Posts: 61 Thanks: 0 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 04:01 AM.
 June 27th, 2013, 06:18 AM #2 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 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 03:52 AM.
 June 13th, 2017, 04:08 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 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.
 June 15th, 2017, 05:22 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 "HK" is, of course, "Hong Kong".

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# 3. Suppose the earth to be a real sphere with the radius R. The arc distance from HK (N23) to the North pole is:

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