Chapter 13, Problem 10STP

To determine

If an 18 foot ladder leans against the side of a house and base of the ladder is 5 feet from the wall of the house then find the height of the side of house where the ladder reaches.

Answer to Problem 10STP

The height of the wall is $12\text{ ft}$ , so ladder will reach at a height of $12\text{ ft}$ .

Explanation of Solution

Given information: The ladder is 18 foot long which leans against the wall of a house and the ladder is 5 feet from the bottom of the wall.

Calculation: The possible diagram for the wall and ladder is shown as, therefore by Pythagoras Theorem the height $\left(AB\right)$ of the wall is evaluated as,

  

  $\begin{array}{c}AB=\sqrt{A{C}^2-B{C}^2}\\ =\sqrt{{\left(17\right)}^2-{\left(5\right)}^2}\\ =12\text{ft}\end{array}$

Hence the height of the wall is $12\text{ ft}$ .