Prove Heron's Formula (Trigonometry)

[rocomath]

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​

 

[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)<

 

[rocomath]

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!

 

[rootX]

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

 

[rocomath]

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

ok let me try it that way.