THE PYTHAGOREAN THEOREM. PYTHAGOREAN THEOREM REAL LIFE EXAMPLE The ... - Free Printable

Great! Let's walk through this real-life example step by step and verify the solution.

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🔧 Problem Statement:

A 16-foot ladder is placed against a wall. According to a rule of thumb, the bottom of the ladder should be one-fourth the length of the ladder away from the wall.

So:
- Length of ladder = 16 ft → so distance from wall = $ \frac{1}{4} \times 16 = 4 $ ft.
- We want to find how high up the wall the ladder reaches — that is, the vertical height $ x $.

This forms a right triangle, where:
- The ladder is the hypotenuse ($ c = 16 $ ft),
- The base (distance from wall) is $ a = 4 $ ft,
- The height up the wall is $ b = x $ ft (unknown).

We use the Pythagorean Theorem:

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

Substitute values:

$$
4^2 + x^2 = 16^2
$$

$$
16 + x^2 = 256
$$

Now subtract 16 from both sides:

$$
x^2 = 256 - 16 = 240
$$

Now take the square root:

$$
x = \sqrt{240}
$$

Let’s simplify:

$$
\sqrt{240} = \sqrt{16 \times 15} = 4\sqrt{15} \approx 4 \times 3.873 = 15.492
$$

So:

$$
x \approx 15.49 \text{ feet}
$$

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✔ Final Answer:

The ladder will reach approximately 15.49 feet up the wall.

> ✔️ Your handwritten work is correct!

You wrote:
- $ x = \sqrt{240} $
- $ x \approx 15.49 $

And you correctly used the Pythagorean Theorem.

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📌 Summary:

- Given: 16-ft ladder, 4 ft from wall
- Find: Height on wall
- Used: $ a^2 + b^2 = c^2 $
- Result: $ x \approx 15.49 $ ft

✔ This is a practical application of right triangles in construction and safety!

Let me know if you'd like to explore what happens with different ladder lengths or angles!