# Prove Heron's Formula (Trigonometry)

1. Aug 26, 2007

### rocomath

1. The problem statement, all variables and given/known data

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.

3. 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.

Last edited: Aug 26, 2007
2. Aug 26, 2007

### rootX

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. Aug 26, 2007

### rocomath

lol ... i don't follow!!! :surprised

4. Aug 26, 2007

### rootX

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

5. Aug 26, 2007

### rocomath

ok let me try it that way.