Unformatted text preview: △ ABC with sides a , b , and c , let s = 1 2 ( a + b + c ) (i.e. 2 s = a + b + c is the perimeter of the triangle). Then the area K of the triangle is Area = K = r s ( s − a )( s − b )( s − c ) . (2.29) To prove this, ±rst remember that the area K is onehalf the base times the height. Using c as the base and the altitude h as the height, as before in Figure 2.4.1, we have K = 1 2 hc . Squaring both sides gives us K 2 = 1 4 h 2 c 2 . (2.30) 7 Note that this is equivalent to knowing just two angles and a side (why?). 8 Due to the ancient Greek engineer and mathematician Heron of Alexandria (c. 1070 A.D.)....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Angles

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