Chapter 1 - Equations and Inequalities - 1.5 Applications and Modeling with Quadratic Equations - 1.5 Exercises - Page 132: 42

$4.55\ ft$

Step 1. Assume the height of the break is $x\ ft$ Step 2. The length of the hypotenuse can be found as $10-x$ Step 3. Use Pythagorean theorem, we have $(10-x)^2=(x)^2+(3)^2$ Step 4. Solve the above equation to get $100-20x+x^2=x^2+9$ which gives $x=\frac{91}{20}=4.55\ ft$