Question

Fie ABCD un romb si O , intersectia diagonalelor sale. Sa se calculeze sin(BAD), stiind ca     AB + BO = AC.

Answer 1

Notam Ab=a,AO=b si BO=c, x=<BAO.
Au loc relatiile;
$b^2+c^2=a^2,a+c=2b,sinx= \frac{c}{a}$
c=2b-a
[tex]b^2+(2b-a)^2=a^2\\ 5b=4a\\ b= \frac{4a}{5} \\ c= \frac{8a}{5} -a= \frac{3a}{5} \\ sin2x=2 \cdot sinx\cdot cosx=2\cdot \frac{c}{a} \cdot \frac{b}{a}= \frac{24}{25} [/tex]
In concluzie, sin(BAD)=24/25.