SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Length\text{ of Arc = }\frac{\theta}{360^0}\text{ x 2 }\pi\text{ r} \\ Here,\text{ Arc of length = 6 inches} \\ Radiu\text{s = x} \\ \theta\text{ = 113}^0 \end{gathered}[/tex][tex]\begin{gathered} 6\text{ = }\frac{113^0}{360^0}\text{ x 2 x }\pi\text{ x \lparen x\rparen} \\ cross\text{ - multiply, we have that:} \\ 6\text{ x 360 = 113 x 2 x }\pi\text{ x \lparen x\rparen} \\ Making\text{ x the subject of the formulae, we have that:} \end{gathered}[/tex][tex]\begin{gathered} \text{x =}\frac{6\text{ x 360}}{113\text{ x 2 x }\pi} \\ x\text{ = }\frac{2160}{709.9999397} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = 3.042253779} \\ x\text{ }\approx\text{ 3.0 inches \lparen to the nearest tenth of an inch \rparen} \end{gathered}[/tex]
CONCLUSION:
The length of the radius, x, ( to the nearest tenth of an inch) = 3.0 inches
