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Prove Heron's Formula (Trigonometry)

  • Thread starter rocomath
  • Start date
  • #1
1,752
1

Homework Statement



If a, b, c are the lengths of the sides of a triangle, then the area K of the triangle is given by [tex]K=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{1}{2}(a+b+c)[/tex]. The number s is called the semiperimeter. Prove Heron's Formula. Hint: Use the area formula [tex]K=\frac{1}{2}bc\sin\phi[/tex].

sinphi should be sinA. it wouldn't let me use sinA.

The Attempt at a Solution



Absolute torture if you ask me!!! I need help getting on the right track, any help is appreciated.

Ignore everything from the triangle and down, that's a different problem.

http://img206.imageshack.us/img206/697/53149485pi4.jpg [Broken]​
 
Last edited by a moderator:

Answers and Replies

  • #2
378
2
my way:
K=whatever
K^2=whatever without sqrt

K^2 = that sin theta area^2

and using identidy sin^2 = 1-cos^2 in above

and cosine law, and some simplication, you would eventually reach somewhere like
-a^4+6a^3+3a^2......

and now just expand that herione thing

lol >(evil smile)<
 
  • #3
1,752
1
my way:
K=whatever
K^2=whatever without sqrt

K^2 = that sin theta area^2

and using identidy sin^2 = 1-cos^2 in above

and cosine law, and some simplication, you would eventually reach somewhere like
-a^4+6a^3+3a^2......

and now just expand that herione thing

lol >(evil smile)<
lol ... i don't follow!!! :surprised
 
  • #4
378
2
you didn't square the equation in the starting, but I did..
 
  • #5
1,752
1
you didn't square the equation in the starting, but I did..
ok let me try it that way.
 

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