Question

pythagorean theorem word problems draw a picture and then use the pythagorean theorem to solve for the missing side. 1. the bottom of a ladder must be placed 3 feet from a wall. the ladder is 10 feet long. how far above the ground does the ladder touch the wall?

Explanation:

Step1: Identify the sides

Let the distance from the bottom of the ladder to the wall be \( a = 3 \) feet (one leg of the right triangle), the length of the ladder be \( c = 10 \) feet (hypotenuse), and the height on the wall be \( b \) (the other leg we need to find). The Pythagorean theorem is \( a^{2}+b^{2}=c^{2} \).

Step2: Rearrange the formula

We need to solve for \( b \), so rearrange the formula: \( b^{2}=c^{2}-a^{2} \).

Step3: Substitute the values

Substitute \( a = 3 \) and \( c = 10 \) into the formula: \( b^{2}=10^{2}-3^{2}=100 - 9=91 \).

Step4: Solve for \( b \)

Take the square root of both sides: \( b=\sqrt{91}\approx9.54 \) feet.

Answer:

The ladder touches the wall approximately \(\boldsymbol{\sqrt{91}\text{ feet (or about } 9.54 \text{ feet)}}\) above the ground.