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 06-29-2006, 12:14 AM #1 Member   Join Date: Mar 2006 Posts: 406 Math Question Math question Guys- i vaguely remember a formula that is usd to find the third side of a triangle when all you're given is two sides(not a 30,60,90 or 45,45,90)... its like: S= a+b+c/ 2 It's a method used to find the third side----know what i'm talkin 'bout? Reply
 06-29-2006, 12:20 AM #2 Senior Member   Join Date: Oct 2005 Location: New York City, NY Posts: 1,017 are you sure that's the question? Because according to you, we know s, a, and b, so just use 2s - a - b = c. Reply
 06-29-2006, 12:22 AM #3 Senior Member   Join Date: Oct 2005 Location: New York City, NY Posts: 1,017 you might mean huron's formula for areas = A = sqrt [(S)(s-a)(s-b)(s-c)] Reply
 06-29-2006, 12:36 AM #4 Member   Join Date: Mar 2006 Posts: 406 thats definitely it...thanks..i remember the sqrt. S(s-a)(s-b)(s-c) part. But i think the first part of the method it to write this out- S= a+b+c/ 2 -I dont know if its necesary though...I always thought there was a franction in there somewhere...anyway.. how do you use it to find the third side? Reply
 06-29-2006, 12:37 AM #5 Senior Member   Join Date: Oct 2005 Location: New York City, NY Posts: 1,017 i really don't know unless u knew the area, and the semi perimeter as well as the two sides. Reply
 06-29-2006, 12:48 AM #6 Member   Join Date: Mar 2006 Posts: 406 I wanted to use it to solve this question...I got the answer right but i'm just curious to knwo if that formula can be used.Maybe you can test the trhee areas. 3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle? I 24 II 20 III 5 A. I only B. II only C. III only D. II and III only E. I, II and III Reply
 06-29-2006, 12:49 AM #7 Junior Member   Join Date: Jun 2006 Posts: 201 you can find the third side of the triangle using trigonometry, if you have the angle between the known sides Reply
 06-29-2006, 12:54 AM #8 Member   Join Date: Mar 2006 Posts: 406 trip- you dont---i've edited my previous post and included the question. I know its an easy question but i want to see if i can solve it using a definite method rather than using logic. Reply
 06-29-2006, 01:35 AM #9 Member   Join Date: Apr 2006 Posts: 583 The "S" in S=a+b+c/2 simply stands for semiperimeter, which makes sense. Herons is given above but it only useful if you have all three side lengths of a triangle. That being said, what you could do is use the triangle inequality (two sides of a triangle must be greater than third side) to find the min and max values of the third side, plug each of the two with 5 and 8 (other two sides) into herons, and get an area inequality. Personally I haven't tried that (similar prob. in red book, used logic), but this type of problem would definitely be one of the last ones on a math section if not the very last, so it MIGHT work. For me, logic is the definite method. Reply
 06-29-2006, 02:22 AM #10 Member   Join Date: Apr 2006 Posts: 394 The area of a triangle is 0.5bh (b=base, h=height). With the longer side as the base (i.e., b=8), the height must be greater than zero but less than or equal to 5. So, A=0.5x8xh with 0

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