ABC este triunghiul dreptunghic. unghiul A este unghiul drept
fie AN mediana triunghiului ABC=> AN= BC/2=> AN=25/2
daca AN mediana=> AN=CN=NC=BC/2=> AN =CN=NB=25/2
fie AM inaltime => unghiul AMN=90 grade
(DACA AM INALTIME SI AN MEDIANA, UNGHIUL FORMATDE INATIME SI MEDIANA ESTE UNGHIUL MAN=30 GRADE-VEZI IPOTEZA )
in Δ AMN:
am aflat AN=25/2
avem unghi MAN=30
aplic teorema unghiului de 30 grade=> MN=AN=2=> AM=25/2/2=>MN=25/2:2=>MN=25/2X1/2=>MN=25/4
acum aplic teorema lui Pitagora:
AM²+MN=AN²
AM²+(25/4)²=(25/2)²
AM²+625/16=625/4
AM²=625/4-625/16 (aduc la acelasi numitor)
AM²=625X4/16-625/16
AM²=2500/16-625/16
AM²=1875/16
AM=√1875/16=>AM=25√3/4
In ΔABC:
Teorame catetei:
AB²=BM X CM
BM=BN+MN
BM=25/2+25/4 (aduc la acelasi numitor)
BM=25X2/4+25/4
BM=50/4+25/4
BM=75/4
CM=CN-MN
CM=25/2-25/4 (aduc la acelasi numitor)
CM=25X2/4-25/4
CM=50/4-25/4
CM=25/4
AM²=BM X CM=>AB²= 75/4 X 24/4=>AB²=1875/16=> AB=√1875/16=> AB=25√3/4
teorema lui Pitagora:
AB²+AC²=BC²
(25√3/4)²+AC²=25²
(√1875/4)²+AC²=625
1875/16+AC²=625
AC²=625-1875/16 (aduc la acelasi numitor)
AC²=625 X16/16-1875/16
AC²=10000/16-1875/16
AC²=8125/16
AC=√8125/16=> AC=25√13/4
