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**Unformatted text preview: **e 762 Applications of Trigonometry minimizes the chances of propagated error.3 Third, since many of the applications which require
solving triangles ‘in the wild’ rely on degree measure, we shall adopt this convention for the time
being.4 The Pythagorean Theorem along with Theorems 10.4 and 10.10 allow us to easily handle
any given right triangle problem, but what if the triangle isn’t a right triangle? In certain cases,
we can use the Law of Sines to help.
Theorem 11.2. The Law of Sines: Given a triangle with angle-side opposite pairs (α, a), (β, b)
and (γ, c), the following ratios hold
sin(α)
sin(β )
sin(γ )
=
=
a
b
c
The proof of the Law of Sines can be broken into three cases. For our ﬁrst case, consider the
triangle ABC below, all of whose angles are acute, with angle-side opposite pairs (α, a), (β, b)
and (γ, c). If we drop an altitude from vertex B , we divide the triangle into two right triangles:
ABQ and B CQ. If we call the length of the altitude h (for height), we get from Theorem 10.4
that sin(α) = h and sin(γ ) = h so that h = c sin(α) = a...

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