Unformatted text preview: sin(45◦ ) = 7 3 6 ≈ 5.72 units. Now that
b
7
sin(120
we have two angleside pairs, it is time to ﬁnd the third. To ﬁnd γ , we use the fact that the
sum of the measures of the angles in a triangle is 180◦ . Hence, γ = 180◦ − 120◦ − 45◦ = 15◦ .
To ﬁnd c, we have no choice but to used the derived value γ = 15◦ , yet we can minimize the
propagation of error here by using the given angleside opposite pair (α, a). The Law of Sines
◦
◦
◦)
gives us sin(15 ) = sin(120 ) so that c = 7 sin(15◦ ) ≈ 2.09 units. We sketch this triangle below.
c
7
sin(120
2. In this example, we are not immediately given an angleside opposite pair, but as we have
the measures of α and β , we can solve for γ since γ = 180◦ − 85◦ − 30◦ = 65◦ . As in the
previous example, we are forced to use a derived value in our ◦computations since the only
◦
angleside pair available is (γ, c). The Law of Sines gives sin(85 ) = sin(65 ) . After the usual
a
5.25
◦
rearrangement, we get a = 5.25 sin(85 ) ≈ 5.77 units. To ﬁnd b we use the angleside pair (γ,...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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