notez inaltimea din B cu BHAC=15BC=12
a)triunghiuri asemenea:ABC cu ABH, unghiuri congruente (∡A comun, ∡ABH=90-∡A=∡C)
ABC cu BHC, unghiuri congruente (∡C comun, ∡HBC=90-∡C=∡A)
b)
cu pitagora in ABC
AB^2=AC^2-BC^2
AB^=15^2-12^2=81
AB=9
c)
cos C=BC/AC=12/15=4/5
cos A=AB/AC=9/15=3/5
d)
AC x BM=AB x BC (aria ABC in 2 moduri)
BM=9 x 12/15
BM=36/5
e)
teorema catetei AB
AB^2=AH x AC
81=AH x 15
AH=27/5
tg HBA=AH/BH=27/5 x 5/36=3/4
tg HBC=HC/BH=(AC-AH)/BH=48/5 x 5/36=4/3
