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 AngleSideSide (ASS) case if you can avoid it?
7
Again, y...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details