# Prove Heron's Formula (Trigonometry)

## 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 $$K=\sqrt{s(s-a)(s-b)(s-c)}$$, where $$s=\frac{1}{2}(a+b+c)$$. The number s is called the semiperimeter. Prove Heron's Formula. Hint: Use the area formula $$K=\frac{1}{2}bc\sin\phi$$.

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]​

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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)<

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

you didn't square the equation in the starting, but I did..

you didn't square the equation in the starting, but I did..
ok let me try it that way.