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 (Tetrahedron)
This solution refers to the Diagram section.
Let be the orthogonal projection of
onto the equator. Note that
and
Let For tetrahedron
- Since
is an isosceles right triangle, we have
- In
we apply the Law of Cosines to get
- In right
we apply the Pythagorean Theorem to get
- In
we apply the Law of Cosines to get
from which
degrees.
~MRENTHUSIASM
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
IN CONSTRUCTION ... NO EDIT PLEASE ... WILL FINISH BY TODAY ...
Solution 3 (Coordinate Geometry)
IN CONSTRUCTION ... NO EDIT PLEASE ... WILL FINISH BY TODAY ...
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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