Chapter 9.6, Problem 20E

To determine

To find the size of a wrench that is close to the distance across the nut from one edge to the opposite edge.

Answer to Problem 20E

The size of a wrench that is close to the distance across the nut from one edge to the opposite edge $=\frac{7}{16}inch$

Explanation of Solution

Given: Each edge of the nut has a length of $\frac{1}{4}inch.$

  

Calculation:

The size of a wrench that is close to the distance across the nut from one edge to the opposite edge can be obtained as:

  $\begin{array}{l}\sin {60}^0=\frac{opposite}{hypotenuse}=\frac{a}{1/4}=4a\\ \Rightarrow a=\sin {60}^0/4\\ =0.2165\\ \approx 0.22Inches.\\ And\text{ b also equal to }0.22Inches\text{ because the distance a and b are equal}\text{.}\\ \text{So, b = a = 0}\text{.22 Inches}\text{.}\\ \text{Hence the total height of the wrench = a+b = 0}\text{.22+0}\text{.22 =0}\text{.44 Inches}\text{.}\end{array}$

But the sizes to be found are:

  $\begin{array}{l}\frac{3}{8}inch=0.375inch\\ \frac{7}{16}inch=0.4375\approx 0.44inch\\ \frac{1}{2}inch=0.5inch\\ Hence,\text{ the size of wrench chosen = 0}\text{.44inch=}\frac{7}{16}inch.\end{array}$