Chapter 4.8, Problem 46E

To determine

Find the length of sides of a regular hexagon inscribed in a circle of radius 25 inches.

Answer to Problem 46E

The length of sides of a hexagon inscribed in a circle is also 25 inches.

Explanation of Solution

Given:

Radius of circle = 25inches.

  

Using the following formula in a $△ABC$

  $\begin{array}{l}{a}^2=b^2+c^2-2bc\cos A\hfill \\ \text{ Where }b=c=r\text{ and }A={60}^{°}\hfill \end{array}$

Therefore

  $a^2=r^2+r^2-2rr\cos \left({60}^{\circ }\right)$

  $\begin{array}{cc}{a}^2& =r^2+r^2-2rr(1/2)\\ a^2& =r^2+r^2-r^2\\ a^2& =r^2\\ a& =r\end{array}$

Thus, the length of the sides of the regular hexagon inscribed in a circle is equal to the radius of the circle

since the radius of the circle is 25 inches, therefore the length of sides of a hexagon inscribed in a circle is also 25 inches.