Answer:
[tex]a=9\ in\\b= 9\ in[/tex]
Step-by-step explanation:
This straight triangle has two angles equal to 45 ° and two equal sides.
We know that the side opposite the 90 degree angle is:
[tex]c =9\sqrt{2}\ in[/tex]
Since the triangle has two equal angles, then it is an iscoceles triangle.
This means that
[tex]a = b[/tex]
We use the Pythagorean theorem to find b
[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]
