Triangles Formulas
I - On connait
les 3 Cotés (a,b,c)
P=(a+b+c)/2
TAN(A/2)=RACINE((p-b)*(p-c)/p*(p-a))
|
||
a/SIN(A)=b/SIN(B)=c/SIN©=2R
|
||
S=RACINE(p*(p-a)*(p-b)*(p-c))
|
||
II -On connait 1 angle et 2 Cotés Adjacents (b,c,A)
a^2=B^2+C^2-2*b*c*COSA
|
||
TAN(B-C)/2=(b-c)/(b+c)*COT(A/2)
|
||
S=1/2a*b*SIN(C )=abc/4R=rP
|
||
A+B+C=200
|
||
III -2 angle et le coté commun (B,C,a)
A=200-B-C
|
||
S=1/2*a^2*SIN(B)*SIN(C)/SIN(B+C)
|
||
IV -1 angle et 2 Cotés (A,a,c)
a/SINA=b/SINB=c/SINC
|
|
C=200-ASIN(c*SINA/a)
|
|
b=aSINB/SIN(B+C)
|
|
S=1/2*c^2*(SINA*SINB)/SIN(A+B)
| |
