Question

VA ROG 1,2 DAU COROANA!!!​

Answer 1

Salut!

1. Aria unui romb este de 120 m², iar una dintre diagonale are 10 m. Aflati latura rombului.

Voi nota rombul ABCD, diagonalele sunt AC, BD. Laturi: AB,BC,CD,DA. Fie {O}=AC∩BD. Si BD=10.

$Aria=\frac{d_1*d_2}{3} \\\\120=\frac{BD*AC}{2}\\\\120=\frac{10*AC}{2}\\\\120=5AC|:5\\\\AC=24$

Deci AO=OC=12  si  BO=OD=5

Pitagora in ΔAOB:

AB²=AO²+OB²

AB²=12²+5²

AB²=144+25

AB²=169

AB=√169

AB=13

2. Aria unui triunghi dreptunghic ABC, cu ∡A-drept este de 24 m², iar AB=8 m. Calculati sin B.

$Aria=\frac{c_1*c_2}{2} \\\\24=\frac{AB*AC}{2} \\\\24=\frac{8*AC}{2} \\\\24=4*AC|:4\\\\AC=6$

In ΔABC-Pitagora

BC²=AC²+AB²

BC²=6²+8²

BC²=36+64

BC²=100

BC=√100

BC=10

$sin B=\frac{cat.op.}{ip.}\\\\sinB=\frac{AC}{BC} \\\\sinB=\frac{6}{10} \\\\sinB=\frac{3}{5}$

Succes!