Question: Using Pythagoras' theorem, calculate the length of $YZ$. Give your answer to 1~d.p.
$5$ cm
$17$ cm
$X$
$Y$
$Z$
The diagram is a right-angled triangle with the right angle at $Y$, top side $XY = 5$ cm, slanted side $XZ = 17$ cm, and vertical side $YZ$ unknown; position_hint = center.
1. **Problem statement:** We have a right-angled triangle $XYZ$ with the right angle at $Y$. The side $XY$ is $5$ cm, the hypotenuse $XZ$ is $17$ cm, and we need to find the length of side $YZ$.
2. **Formula:** According to Pythagoras' theorem for a right triangle,
$$XZ^2 = XY^2 + YZ^2$$
where $XZ$ is the hypotenuse.
3. **Substitute known values:**
$$17^2 = 5^2 + YZ^2$$
4. **Calculate squares:**
$$289 = 25 + YZ^2$$
5. **Isolate $YZ^2$:**
$$YZ^2 = 289 - 25$$
$$YZ^2 = 264$$
6. **Find $YZ$ by taking the square root:**
$$YZ = \sqrt{264}$$
7. **Simplify and approximate:**
$$YZ \approx 16.2481$$
8. **Round to 1 decimal place:**
$$YZ \approx 16.2$$ cm
**Final answer:** The length of $YZ$ is approximately $16.2$ cm.