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To solve for the unknown length \( y \) in the given diagram, we can use the Pythagorean theorem, as the setup involves a right triangle.

From the diagram:
- The vertical side (rise) is \( 5 \, \text{ft} \),
- The horizontal side (run) is \( 19 \, \text{ft} \),
- The slant length, which appears to be the hypotenuse, is unknown and labeled as \( y \).

Using the Pythagorean theorem:

\[
y^2 = 5^2 + 19^2
\]

Let me calculate \( y \).The unknown length \( y \), which is the hypotenuse of the right triangle, is approximately \( 19.65 \, \text{ft} \).

Would you like further details or have any questions?

Here are some related questions:
1. What is the formula for the Pythagorean theorem?
2. How can you apply the Pythagorean theorem in 3D space?
3. What are some practical uses of right triangles in construction?
4. Can the Pythagorean theorem be used with non-right triangles?
5. How do we approximate the square root of non-perfect squares by hand?

**Tip:** When dealing with measurements in diagrams, always check if the dimensions form a right triangle to apply the Pythagorean theorem effectively.

Find the unknown length y in the given diagram.

Learn how to use the Pythagorean theorem to find the unknown length of a ramp. This geometry problem involves a right triangle where the rise is 5 feet, the run is 19 feet, and the slanted length is the unknown variable y. Suitable for students in Grades 8-10.

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