Chapter 8.4, Problem 38WE

To determine

To find: the value of x for wrench.

Answer to Problem 38WE

The value of x is $\sqrt{3}\text{cm}$ .

Explanation of Solution

Given:

The wrench is shown below:

  

Side of hexagonal nut is 1 cm.

Calculation:

Hexagon nut is shown below:

  

In triangle ABC ,

  $\begin{array}{c}\sin 60°=\frac{BC}{AB}\\ \frac{BC}{1}=\frac{\sqrt{3}}{2}\\ BC=\frac{\sqrt{3}}{2}\text{cm}\end{array}$

Side BD is twice of side BC .

Hence,

  $\begin{array}{c}BD=2BC\\ =2\left(\frac{\sqrt{3}}{2}\text{cm}\right)\\ =\sqrt{3}\text{cm}\end{array}$

Hence, the value of x is $\sqrt{3}\text{cm}$ .