2018 AMC 12B Problems/Problem 23
Contents
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
Diagram
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Solution 1 (Law of Cosines)
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Solution 2 (Coordinate Geometry)
Suppose that Earth is a unit sphere with center We can let
The angle
between these two vectors satisfies
yielding
or
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Solution 3 (Coordinate Geometry)
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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 |
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