HW 2 Solutions

# HW 2 Solutions - Math E-21a Fall 2009 HW#2 Solutions Proof...

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1 Math E-21a – Fall 2009 – HW #2 Solutions Proof of the Pythagorean Theorem – Perhaps the easiest way to prove this is with areas: c c c c a a a a b b b b The area of the larger square is the sum of the areas of the smaller square and the four right triangles. This gives us:  22 1 2 2 22 2 () 4 ab c a b aa b b ca b abc   Proof of the Law of Cosines – Referring to the variables in the diagram, this is a straightforward application of algebra and basic trigonometry: 2 Bmh and 222 Chn  Amn , so we can write nAm  . If we substitute this, we get:

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HW 2 Solutions - Math E-21a Fall 2009 HW#2 Solutions Proof...

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