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**Unformatted text preview: **lt; h, then a < c sin(α). If a triangle were
to exist, the Law of Sines would have sin(γ ) = sin(α) so that sin(γ ) = c sin(α) > a = 1, which is
c
a
a
a
impossible. In the ﬁgure below, we see geometrically why this is the case. c a c
h = c sin(α) α a < h, no triangle a = h = c sin(α)
α a = h, γ = 90◦ Simply put, if a < h the side a is too short to connect to form a triangle. This means if a ≥ h,
we are always guaranteed to have at least one triangle, and the remaining parts of the theorem
tell us what kind and how many triangles to expect in each case. If a = h, then a = c sin(α) and
7 If this sounds familiar, it should. From high school Geometry, we know there are four congruence conditions for
triangles: Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), Side-Angle-Side (SAS) and Side-Side-Side (SSS). If we
are given information about a triangle that meets one of these four criteria, then we are guaranteed that exactly one
triangle exists which satisﬁes the given criteria.
8
In more reputable books, this is called the ‘Side-Side-Angle’ or S...

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