Engineering Calculus Notes 31

Engineering Calculus Notes 31 - Denote the length of CD by...

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1.1. LOCATING POINTS IN SPACE 19 proofs.” A second approach is via the theory of proportions. Here is an example: again, suppose ABC has a right angle at C ; label the sides with lower-case versions of the labels of the opposite vertices (Figure 1.14 ) and draw a perpendicular CD from the right angle to the hypotenuse. This cuts the hypotenuse into two pieces of respective lengths c 1 and c 2 , so c = c 1 + c 2 . (1.12)
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Unformatted text preview: Denote the length of CD by x . C A B a b c 1 c 2 Figure 1.14: Pythagoras Theorem by Proportions (a) Show that the two triangles ACD and CBD are both similar to ABC . (b) Using the similarity of CBD with ABC , show that a c = c 1 a or a 2 = cc 1 . (c) Using the similarity of ACD with ABC , show that c b = b c 2 or b 2 = cc 2 ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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