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Unformatted text preview: ond triangle predicted in the theorem. To prove the last case in the theorem, we
assume a ≥ c. Then α ≥ γ , which forces γ to be an acute angle. Hence, we get only one triangle
in this case, completing the proof. c a a
c α γ0 γ0 h < a < c, two triangles a h
α γ a ≥ c, one triangle One last comment before we use the Law of Sines to solve an application problem. In the AngleSide-Side case, if you are given an obtuse angle to begin with then it is impossible to have the two
triangle case. Think about this before reading further.
Example 11.2.3. Sasquatch Island lies oﬀ the coast of Ippizuti Lake. Two sightings, taken 5 miles
apart, are made to the island. The angle between the shore and the island at the ﬁrst observation
point is 30◦ and at the second point the angle is 45◦ . Assuming a straight coastline, ﬁnd the
distance from the second observation point to the island. What point on the shore is closest to the
island? How far is the island from this point?
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