Question

5 fill in the blank 1 point if $y = 20sqrt{2}$, find $x$ and $z$. $x =$ choose your answer... $z =$ choose your answer...

Explanation:

This is a 45 - 45 - 90 right triangle, where the legs are equal (\(x = z\)) and the hypotenuse \(y\) is related to the legs by the formula \(y=x\sqrt{2}\) (or \(y = z\sqrt{2}\)).

Step 1: Find \(x\) (and \(z\) since \(x = z\) in a 45 - 45 - 90 triangle)

We know the formula for the hypotenuse \(y\) in a 45 - 45 - 90 triangle is \(y=x\sqrt{2}\), and we are given that \(y = 20\sqrt{2}\).
We can solve for \(x\) by rearranging the formula:
\(x=\frac{y}{\sqrt{2}}\)
Substitute \(y = 20\sqrt{2}\) into the formula:
\(x=\frac{20\sqrt{2}}{\sqrt{2}}\)
The \(\sqrt{2}\) terms in the numerator and denominator cancel out, so \(x = 20\).

Since in a 45 - 45 - 90 triangle the two legs are equal, \(z=x\), so \(z = 20\).

Answer:

\(x=\boldsymbol{20}\), \(z=\boldsymbol{20}\)