Question

Pythagorean Theorem Word Problems.The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall.

Answer 1

11.62 ft

Step-by-step explanation

First, we have to make a sketch of the problem:

We have the ladder resting on the wall.

We need to find the value of x, the height of the ladder from the ground.

Using Pythagoras theorem, we have that:

`\begin{gathered} \text{hyp}^2=a^2+b^2 \\ \text{where a and b are legs of the triangle} \\ \Rightarrow12^2=x^2+3^2 \\ \Rightarrow x^2\text{ = 144 - 9} \\ x^2\text{ = }135 \\ x\text{ = }\sqrt[]{135} \\ x\text{ =11.62 ft} \end{gathered}`

The ladder must touch the wall 11.62 feet above the ground.