Question

45° 9√2 b a

Explanation:

Step1: Identify the triangle type

This is a 45 - 45- 90 right - triangle. In a 45 - 45- 90 triangle, the ratio of the sides is $a:b:hypotenuse = x:x:x\sqrt{2}$.

Step2: Set up the equation

Given that the hypotenuse is $9\sqrt{2}$, and the hypotenuse in a 45 - 45- 90 triangle is $x\sqrt{2}$. So we set $x\sqrt{2}=9\sqrt{2}$.

Step3: Solve for $x$

Dividing both sides of the equation $x\sqrt{2}=9\sqrt{2}$ by $\sqrt{2}$, we get $x = 9$. Since $a$ and $b$ are the legs of the 45 - 45- 90 triangle and are equal, $a=b = 9$.

Answer:

$a = 9$, $b = 9$