2007-03-31 22:45:26 · 6 answers · asked by Rishu 1 in Science & Mathematics ➔ Mathematics
Step by step proof of Heron's formula
agutie.homestead.com/files/Heron/index.html
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2007-04-01 02:59:35 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
Start from
Area = (1/2)ab sin C
Now sin C = â(1-(cos C)^2)
Using the cosine rule, the expression under the â sign becomes
1 - [(a^2 + b^2 - c^2)/(2ab)]^2
Factorise by difference of squares and at the same time (to save a line of this pesky typing of Mathematics symbols) use 4(a^2)(b^2) as common denominator:
[ (2ab + (a^2 + b^2 -c^2))(2ab - (a^2 + b^2 - c^2))]/(2ab)^2
The numerator of this fraction is
((a+b)^2 - c^2)(c^2 - (a-b)^2)
= (a+b+c)(a+b-c)(c+a-b)(c-a+b)
If a+b+c = 2s, these factors become
2s * 2(s-c) * 2(s-b) * 2(s-a)
Divide by (2ab)^2, take the square root, and multiply by ab/2, and get Hero's formula.
2007-03-31 23:00:22 · answer #2 · answered by Hy 7 · 1⤊ 0⤋
In my opinion you should search the mathematics book of IX standard of NCERT. You would get your answer.
Good Luck
2007-04-01 03:57:39 · answer #3 · answered by Anonymous · 0⤊ 0⤋
hey why are you desperate to learn this when derivation is not in the course
2007-04-01 01:22:28 · answer #4 · answered by Sam 2 · 0⤊ 0⤋
its on wiki
2007-03-31 22:50:06 · answer #5 · answered by hustolemyname 6 · 0⤊ 0⤋
Please see:
http://en.wikipedia.org/wiki/heron's_for...
2007-04-01 06:33:52 · answer #6 · answered by $ri 3 · 0⤊ 0⤋