This preview shows page 1. Sign up to view the full content.
Unformatted text preview: The Area of a Triangle Section 2.4 57 Example 2.15 b = 4 a = 5 c = 7 A B C Find the area of the triangle ABC given a = 5, b = 4, and c = 7. Solution: Using Herons formula with s = 1 2 ( a + b + c ) = 1 2 (5 + 4 + 7) = 8, the area K is given by: K = radicalbig s ( s a )( s b )( s c ) = radicalbig 8(8 5)(8 4)(8 7) = radicallow 96 K = 4 radicallow 6 9.8 . Herons formula is useful for theoretical purposes (e.g. in deriving other formulas). How ever, it is not wellsuited for calculator use, exhibiting what is called numerical instability for extreme triangles, as in the following example. Example 2.16 Find the area of the triangle ABC given a = 1000000, b = 999999.9999979, and c = 0.0000029. Solution: To use Herons formula, we need to calculate s = 1 2 ( a + b + c ). Notice that the actual value of a + b + c is 2000000.0000008, which has 14 digits. Most calculators can store 1214 digits internally (even if they display less), and hence may round off that value of...
View Full
Document
 Fall '11
 Dr.Cheun
 Calculus

Click to edit the document details