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In this situation, two cars are racing through a rally course at very high
speeds. The blue car, is being driven by Dante, and the red car is being driven
by Gonzalez. Gonzalez has the option of taking two different paths. One leads
to the water and the other path leads to certain doom for a broken down motorist.
Since Gonzalez and Dante had just left math class, even at high speeds, they thought
that this was an interesting use of the Ambiguous Sine Law!
The situation is represented by the diagram below: |
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| In this situation, we
are given angle A,
and we also know the lengths
of sides c and a.
Both lines, a,
have the same distance.
So, we must know the remaining
dimensions of the triangle,
because of SAS.
But do we??? Gonzalez could
drive on either of the
a paths and it would therefore
be unclear which triangle
would be formed in this
situation. This possibility
of two triangles, given
two sides and the angle
not included, is called
the Ambiguous Sine
Law. |
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