Question

solve for y and x
answer attempt 1 out of 3
y =
x =

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs (the sides opposite the 45° angles) are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg. Let the length of each leg be $a$ and the hypotenuse be $c$. So $c = a\sqrt{2}$.

Step2: Set up equation for hypotenuse

We know that $c = 8\sqrt{2}$, and $c=a\sqrt{2}$. So, $a\sqrt{2}=8\sqrt{2}$.

Step3: Solve for $a$ (which is $x$ and $y$)

Dividing both sides of the equation $a\sqrt{2}=8\sqrt{2}$ by $\sqrt{2}$, we get $a = 8$. Since $x$ and $y$ are the legs of the 45 - 45 - 90 triangle, $x=y = 8$.

Answer:

$y = 8$
$x = 8$