DANE
a,b,γ
punk D polowa "a"
OBLICZ
cos X
Z twierdzenia cosinusow obliczam
c²=a²+b²-2ab cos γ
dlugosc srodkowej d=AD
d²=a²/4+b²-1/2ab cos γ
d=√(a²/4+b²-1/2ab cos γ)
Z trojkata ADB obliczam c=AB
c²=a²/4+d²-1/2ad cosX
2c²=a²/2+2d²-ad cosX
cosX=(a²/2+2d²-2c²)/(ad)
podstawiam za d ,d² i c²
cosX=[a²/2+2(a²/4+b²-1/2ab cos γ)-2c²]/[a√(a²/4+b²-1/2ab cos γ)]
cosX=[a²+2b²-ab cos γ-2c²]/[a√(a²/4+b²-1/2ab cos γ)]
cosX=[a²+2b²-ab cos γ-2a²-2b²+4ab cos γ]/[a√(a²/4+b²-1/2ab cos γ)]
cosX=[3ab cos γ -a²]/[a√(a²/4+b²-1/2ab cos γ)]
Pozdrawiam
