Chapter 8.2, Problem 49HP

To determine

To calculate:

The value of $x$ using the given figure.

Answer to Problem 49HP

The value of $x$ is $5.4$ .

Explanation of Solution

Given information:

  

Calculation:

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

So, with the help of Pythagoras theorem, in the right $△ABD$ , then find the value of $w=AD$ .

  $\begin{array}{l}w=\sqrt{{11.6}^2-{7.5}^2}\\ =\sqrt{134.56-56.25}\\ =\sqrt{78.31}\end{array}$

In the right $△ABD$ , find the value of $v=AC$

  $\begin{array}{l}v=\sqrt{w^2-{15}^2}\\ =\sqrt{{\left(\sqrt{78.31}\right)}^2-{15}^2}\\ =\sqrt{78.31+225}\\ \approx 17.4\end{array}$

In the right $△FEC$ , find the value of $z=EC$

  $\begin{array}{l}z=\sqrt{{13}^2-{2.7}^2}\\ =\sqrt{169-7.29}\\ =\sqrt{161.71}\\ \approx 12.7\end{array}$

Findthe value of $y=AE$

  $\begin{array}{l}y=v-z\\ =17.4-12.7\\ =4.7\end{array}$

In the right $△AEF$ , find the value of $x$

  $\begin{array}{l}x=\sqrt{y^2-{2.7}^2}\\ =\sqrt{{4.7}^2-{2.7}^2}\\ =\sqrt{22.09+7.29}\\ \approx 5.4\end{array}$

Hence, the value of $x$ $5.4$ .