Răspuns:
AB=8×√3
BD=8
CD=4
AD=8
∡B=30°
∡C=60°
Explicație pas cu pas:
T. Pitagora in ΔABC: BC²=AB²+AC²
16²=AB²+8²
AB²=16²-8²=256-64=192
AB=√192=8×√3
sin(∡B)=AC÷BC
sin(∡B)=8÷16=1/2 ⇔∡B = 30°
∡A + ∡B + ∡C=180°
∡C=180°- (∡A + ∡B) = 180° - (90° + 30°) = 180° - 120° =60°
In ΔADC dreptunghic in D, avem
cosin(∡C)=CD÷AC
CD=AC × cosin(∡C)
CD=8 × cosin(60) =8 × 1/2 =4
BD + CD =BC
BD + 4 =16
BD=16-4=12
In ΔABC cu ∡A = 90° aplicam teorema inaltimii:
AD²=BD×CD
AD²=16×4=64
AD=√64=8
