Răspuns:
a)
In ΔAMN
∡AMN = 90° => ΔAMN = dreptunghic
AN = 2AM =>∡MNA = 30° (cnf.T.30°) => ∡MAN = 60°
∡MNA = 30°
∡MAN = 60° } => ∡MBA = 90° (1)
∡MBA = ∡NBC (op.la varf) => ∡NBC = 90° (2)
Din (1) si (2) => AN ⊥ CM
b)
∡AMN = 30° => AM = 2AB = 400m
MB = √(AM² - AB²) = √(160000-40000) = √120000 = 200√3 m
Teorema Inaltimii
MB² = AB×BN
BN = MB²/AB = 120000m²/200m = 600 m