For a triangle $\Delta ABC$, prove that there are real numbers $s_A,s_B,s_C$ so that,

$1. 0<s_A,s_B,s_C<1$

$2. s_A+s_B+s_C=2$

$3. s_A\cos A+s_B\cos B+s_C\cos C=1$

## parameters for cosine of angles in a triangle sum up to 2

### parameters for cosine of angles in a triangle sum up to 2

One one thing is neutral in the universe, that is $0$.

### Re: parameters for cosine of angles in a triangle sum up to

Hint:

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$

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Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

### Re: parameters for cosine of angles in a triangle sum up to

Well, I created this using the same method but I was hoping for a solution with Barycentric coordinate system.

One one thing is neutral in the universe, that is $0$.