Since the given triangle is an isosceles triangle, we get:
[tex]A=B\text{.}[/tex]
Now, we know that the interior angles of a triangle add up to 180 degrees, meaning:
[tex]A+B+90^{\circ}=180^{\circ}.[/tex]
Substituting the first equation in the above equation, and solving for B we get:
[tex]\begin{gathered} B+B+90^{\circ}=180^{\circ}, \\ 2B=90^{\circ}, \\ B=45^{\circ}. \end{gathered}[/tex]
Substituting B=45° in the first equation we get:
[tex]A=45^{\circ}.[/tex]
Finally, to find x we use the Pythagorean theorem:
[tex]11^2+11^2=x^2\text{.}[/tex]
Solving the above equation we get:
[tex]\begin{gathered} x^2=2\cdot11^2, \\ x=\sqrt[]{2\cdot11^2}, \\ x=11\sqrt[]{2}. \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} A=45^{\circ}, \\ B=45^{\circ}, \\ x=11\sqrt[]{2}. \end{gathered}[/tex]
