This problem involves the Pythagorean Theorem because the ladder, the ground, and the wall form a right triangle.

Given:

• The base of the ladder (distance from the wall) = 5 feet
• The height of the roof (vertical height) = 7 feet

Using the Pythagorean Theorem:
$a^2 + b^2 = c^2$ where:

• $a = 5$ ft (base)
• $b = 7$ ft (height)
• $c$ is the ladder length (hypotenuse)

Step 1: Plug in values

$5^2 + 7^2 = c^2$ $25 + 49 = c^2$ $74 = c^2$

Step 2: Solve for $c$

$c = \sqrt{74} \approx 8.6$

Step 3: Round up to the nearest tenth

The minimum ladder length must be 8.6 feet.

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Would you like a detailed diagram or more explanation?

Related Questions:

1. How do you determine the minimum angle at which the ladder should be placed?
2. What if the ground was sloped—how would that affect the ladder length?
3. If the height was doubled, how would the ladder length change?
4. What is the safe angle for ladder placement according to OSHA standards?
5. If the ladder extends beyond the roof edge for safety, how long should it be?

Tip: Always round up in real-world applications to ensure safety margins when using ladders! 🚀