Chapter 12, Problem 11STP

To determine

To calculate:To find how high up the side of the house does the ladder reach.

Answer to Problem 11STP

Theladder can reach $11.3feet$ high up the side of the house.

Explanation of Solution

Given information:Terrance placed as $12$ feet ladder against the side of the house to paint the shutters. The base of the ladder is $4$ feet from the house

Formula Used:

Pythagoras theorem states that in a right triangle ABC, right angled at B we have

  $A{C}^2=A{B}^2+B{C}^2$

Calculation:

Given that Terrance placed as $12$ feet ladder against the side of the house to paint the shutters. The base of the ladder is $4$ feet from the house

Figure can be drawn as follows:

Here, BC is a ladder.

Thus,

  $\begin{array}{l}AC=12feet\\ AB=4feet\end{array}$

How high up the side of the house does the ladder reach can be calculated using Pythagoras theorem,

  $A{C}^2=A{B}^2+B{C}^2$

Substituting the values,

  $\begin{array}{l}{12}^2=4^2+B{C}^2\\ B{C}^2={12}^2-4^2\\ B{C}^2=144-16\\ B{C}^2=128\\ BC=\sqrt{128}\\ BC=11.313\\ BC\approx 11.3feet\end{array}$

Conclusion:

Hence,ladder can reach $11.3feet$ high up the side of the house.