[tex]\displaystyle A=\frac{(a+b)^2}{8}[/tex]
[tex]\displaystyle A=\frac{ab}{2}.[/tex]
[tex]\displaystyle \Rightarrow\frac{(a+b)^2}{8}=\frac{ab}{2}.[/tex]
Notam [tex]t=\text{tg}(BAC).[/tex]
Atunci [tex]t=\frac{b}{a}\Rightarrow b=at[/tex]
Inlocuim: [tex]\displaystyle \frac{(a+at)^2}{8}=\frac{a\cdot at}{2}[/tex]
[tex]\displaystyle \frac{a^2(1+t)^2}{8}=\frac{a^2t}{2}[/tex]
[tex]\displaystyle \frac{(1+t)^2}{4}=t[/tex]
[tex](1+t)^2=4t \\ \\ t^2+2t+1=4t \\ \\ t^2-2t+1=0 \\ \\ (t-1)^2=0\Rightarrow t=1.[/tex]
Deci m(BAC)=45 grade
Prin urmare si m(ABC)=45.
