The triangle depicted in your image appears to be a right triangle, as indicated by the right-angle mark at vertex $P$. The given values are as follows:

• One leg, $ZP = 8$,
• The other leg, $PT = 15$,
• The hypotenuse, $ZT$, is marked as $x$.

We can calculate $x$ using the Pythagorean Theorem, which states: $x^2 = (\text{leg}_1)^2 + (\text{leg}_2)^2$ Substituting the values: $x^2 = 8^2 + 15^2$ $x^2 = 64 + 225$ $x^2 = 289$ $x = \sqrt{289} = 17$

Final Answer:

The length of the hypotenuse $ZT$ is: $x = 17$

Would you like further clarification or additional steps?

Here are some related questions for deeper understanding:

1. How can we verify the Pythagorean Theorem for other triangles?
2. What is the significance of a right triangle in geometry?
3. How can you calculate the area of this triangle?
4. What trigonometric ratios can be derived from this triangle?
5. How does this triangle relate to real-world applications?

Tip: Always double-check triangle dimensions to ensure they satisfy the Pythagorean Theorem.