Difference between revisions of "2018 AMC 12B Problems/Problem 23"
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Revision as of 16:39, 18 June 2018
Problem
Ajay is standing at point 
near Pontianak, Indonesia, 
latitude and 
longitude. Billy is standing at point 
near Big Baldy Mountain, Idaho, USA, 
latitude and 
longitude. Assume that Earth is a perfect sphere with center 
. What is the degree measure of 
?
![\[\textbf{(A) }105 \qquad \textbf{(B) }112\frac{1}{2} \qquad \textbf{(C) }120 \qquad \textbf{(D) }135 \qquad \textbf{(E) }150 \qquad\]](http://latex.artofproblemsolving.com/b/d/6/bd6254dbaf5105170c9ce34b24e5305c7d231542.png)
Solution
Suppose that Earth is a unit sphere with center 
We can let
![\[A=(1,0,0), B=\left(-\frac{1}{2},\frac{1}{2},\frac{\sqrt 2}{2}\right).\]](http://latex.artofproblemsolving.com/8/e/9/8e905a243e290e86b67fa132e76ed69923172625.png)
The angle 
between these two vectors satisfies 
yielding 
or 
See Also
| 2018 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 22 |
Followed by Problem 24 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
