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## How high can ladders safely reach?

How high can ladders safely reach? Safety experts recommend placing a ladder one foot away from a building for every four feet of height. This ratio keeps everyone from homeowners to fire-fighters safe, but it also limits how high they can reach.

Students use the Pythagorean Theorem to determine the maximum height ladders can safely reach and discuss the implications for fire safety and building construction.

### REAL WORLD TAKEAWAYS

• Ladders positioned on the ground should maintain a safe height:distance ratio of 4:1 to be maximally stable.
• Elements of urban design (like the width of streets and the height of buildings) may make a place more or less vulnerable to fire tragedies.

### MATH OBJECTIVES

• Use Pythagorean Theorem to solve real-world problems
• Model real-world scenarios geometrically

Appropriate most times as students are developing conceptual understanding.
Squares, Roots, Irrationals
Squares, Roots, Irrationals
Content Standards 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Mathematical Practices MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.