Question

1. ccss model with mathematics write and solve a real - world problem that involves using the pythagorean theorem or its converse.

Explanation:

Step1: Create a problem

A ladder is leaning against a wall. The base of the ladder is 3 feet from the wall, and the ladder is 5 feet long. How high up the wall does the ladder reach?
Let \(a = 3\) (distance from wall), \(c=5\) (length of ladder). We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), and we need to find \(b\).

Step2: Substitute values

Substitute \(a = 3\) and \(c = 5\) into \(a^{2}+b^{2}=c^{2}\). We get \(3^{2}+b^{2}=5^{2}\), which is \(9 + b^{2}=25\).

Step3: Solve for \(b\)

Subtract 9 from both sides: \(b^{2}=25 - 9=16\). Then take the square root of both sides. Since \(b>0\) (height), \(b = 4\).

Answer:

The ladder reaches 4 feet up the wall.