Trigonometry proofs

[PiLuvah]

Using the laws of cosines, prove that the area of an equalateral triangle can be shown as the s squared radical 3 over 4.

Prove the Law of Cosines.
Prove the Law of Sines.

[Forte]

Problem 1.
Let the side be s. Prove this using Cos A= b²+c²-a²/2bc

Problem 2.
Let triangle ABC with coordinates A(0,0), B(C,0) and C(bCosA,bSinB) {because AC is the radius.} Then use distance formula.

Problem 3.
First, show that the area of a triangle is 1/2(b)(c)Sin A. By the same logic, A= 1/2(ab)Sin C, and A= 1/2(a)(c) Sin B. This is 3 ways of saying the same thing. Make a 3 way equality. Divide by 1/2(a)(b)(c).

[PiLuvah]

How do you tell which is the radius? And why dont we use law of cosines? Is it because we already know all the angles to be 60?

[Forte]

Why it's the radius?
Remember Unit circle? If you still dont understand I can explain it again for you.

And yes, it's already known all the angles are 60.

[PiLuvah]

Yes please do so.

[Forte]

http://regentsprep.org/Regents/math/algtrig/ATT5/indexATT5.htm This site will help a lot.

[Forte]

Oh and, Im assuming you're studying Algebra 2/Trig. So here are hundreds of problems. Practice till your little heart cant practice anymore. http://jmap.org/JMAP_REGENTS_EXAMS.htm