Răspuns:
Explicație pas cu pas:
∠A=90° SI ∠B=30°⇒∠C=180°-(90°+30°)=180°-120°=60°
MN⊥AB⇒∠MNB=90°, cum ∠MBN=30° ⇒ ∠NMB=180°-(90°+30°)=180°-120°=60°
⇒ΔABC~ΔNBM ⇒
[tex]\displaystyle \frac{MB}{BC} =\frac{BN}{AB} =\frac{MN}{AC} \\\\\displaystyle MB=\frac{BC}{3} => BC=3\times MB\\\\\displaystyle \frac{MB}{BC} =\frac{MN}{AC} => \frac{MB}{3\times MB} =\frac{MN}{AC}[/tex]
[tex]\displaystyle \frac{1}{3} =\frac{MN}{AC} =>MN=\frac{AC}{3}[/tex] qed
