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: 18,953 Thanks: 1599 
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: 3,159 Thanks: 866 
"HK" is, of course, "Hong Kong".


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