Math Problem Statement

Find the length of the hypotenuse in the right-angled triangle ZPT where PZ = 4 and PT is unknown.

Solution

The image shows a right-angled triangle ZPT\triangle ZPT, where:

  • PZPZ is the vertical leg, labeled as 4.
  • ZTZT is the hypotenuse, labeled as X.
  • PTPT is the horizontal leg.

Would you like me to find XX or any other specific value? Let me know how you'd like to proceed!

Here are five related questions to expand on this topic:

  1. How do we use the Pythagorean theorem to find the hypotenuse?
  2. If we know PTPT, how do we verify the triangle using the theorem?
  3. What is the sine, cosine, or tangent of one of the angles?
  4. How do we determine the area of the triangle?
  5. Can we apply trigonometry to solve for missing sides?

Tip:

For any right-angled triangle, the Pythagorean theorem states:
a2+b2=c2a^2 + b^2 = c^2
where cc is the hypotenuse.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right-Angled Triangles
Pythagorean Theorem

Formulas

a² + b² = c²

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-10