The problem requires using Pythagoras' theorem to find the length of YZ in the triangle.

Step-by-step Solution:

1. Identify the given values:

   • The triangle is a right triangle with:
     • One leg: $XY = 5 \, \text{cm}$,
     • Another leg: $XZ = 17 \, \text{cm}$,
     • Hypotenuse to be found: $YZ$.

2. Pythagoras' theorem:

   • Formula: $YZ^2 = XY^2 + XZ^2$.

3. Substitute the given values: $YZ^2 = 5^2 + 17^2$ $YZ^2 = 25 + 289$ $YZ^2 = 314$

4. Solve for $YZ$: $YZ = \sqrt{314}$ Using a calculator: $YZ \approx 17.7 \, \text{cm (to 1 decimal place)}.$

Final Answer:

The length of $YZ$ is 17.7 cm.

Would you like further clarification or have additional questions?

Here are 5 related questions to expand your understanding:

1. How is the hypotenuse defined in a right triangle?
2. What happens if one of the legs was missing instead of the hypotenuse? How would you solve it?
3. Can Pythagoras' theorem be applied to non-right triangles? Why or why not?
4. How would you verify your answer geometrically or practically?
5. Can Pythagoras’ theorem be used in 3D geometry? How?

Tip: Always check the units and ensure your calculator is set to the right mode (degrees/radians) for trigonometric problems.