Stitz-Zeager_College_Algebra_e-book

# 46 373 2 to convert the equation 21x2 10xy 331y 2

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Unformatted text preview: ever, if α ≈ 65.01◦ then it follows that γ ≈ 64.99◦ which means α ≈ γ . This doesn’t make sense since a (the side opposite α) has length 7 units while c (the side opposite γ ) has length 2 units. Hence, we are lead to the conclusion that α ≈ 114.99◦ and we ﬁnd via the usual calculations that γ ≈ 15.01◦ .6 2. Here, we are given the lengths of all three sides.7 Since the largest side given is b = 7 units, we 2 2 2 go after angle β ﬁrst. Rearranging b2 = a +2+ c2 − 2ac cos(β ), we ﬁnd cos(β ) = a +cac−b = − 1 , 2 5 so we get β = arccos − 1 radians ≈ 101.54◦ . Proceeding similarly for the remaining two 5 angles, we ﬁnd γ = arccos 5 radians ≈ 44.42◦ and α = arccos 29 radians ≈ 34.05◦ . 7 35 β ≈ 101.54◦ c=5 a=4 γ ≈ 44.42◦ α ≈ 34.05◦ 5 b=7 Your instructor will let you know which procedure to use. It all boils down to how much you trust your calculator. 6 Carl thinks it’s easier to just use Law of Cosines as often as needed. Why wrestle with the ambiguous AngleSide-Side (ASS) case if you can avoid it? 7 Again, y...
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