Question

ABC triunghi dreptunghic in A , AD inaltime , AC=8 , BC=16 , aflati , AB , BD , CD , AD , B , C

Answer 1

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