The image depicts a right-angled triangle where:

• One leg (opposite the right angle) is labeled as $z$ (unknown).
• The other leg is 10 cm.
• The hypotenuse is 18 cm.

To find the value of $z$, we can use the Pythagorean theorem, which is stated as:

$a^2 + b^2 = c^2$

where:

• $a$ and $b$ are the legs of the right triangle, and
• $c$ is the hypotenuse.

Here, $a = z$, $b = 10 \, \text{cm}$, and $c = 18 \, \text{cm}$.

The formula becomes:

$z^2 + 10^2 = 18^2$

Now, let's solve for $z$.The value of $z$ is 15.0 cm when rounded to one decimal place.

Would you like any further details or explanations?

Here are five related questions to consider:

1. How is the Pythagorean theorem applied in real-world scenarios?
2. What are the properties of a right triangle?
3. How can we verify if a given triangle is a right triangle?
4. What are some advanced applications of the Pythagorean theorem in geometry?
5. How does the Pythagorean theorem relate to trigonometry?

Tip: Always make sure that the triangle in question is a right triangle before applying the Pythagorean theorem.