Answer:
Certainly! To solve for the length of \(YZ\) using Pythagoras' theorem, we'll use the formula \(c^2 = a^2 + b^2\), where \(c\) is the hypotenuse (opposite the right angle) and \(a\) and \(b\) are the other two sides.
Given that the length of one side is \(9 \, \text{cm}\), and the length of the hypotenuse (Z) is \(17 \, \text{cm}\), let's denote the length of \(YZ\) as \(x\) (in centimeters).
So, applying Pythagoras' theorem:
\[17^2 = 9^2 + x^2\]
\[289 = 81 + x^2\]
\[x^2 = 289 - 81\]
\[x^2 = 208\]
To find \(x\), we take the square root of both sides:
\[x = \sqrt{208}\]
\[x \approx 14.4 \, \text{cm}\]
Therefore, the length of \(YZ\) is approximately \(14.4 \, \text{cm}\) to 1 decimal place when rounded.