Question

Circle O shown below has an arc of length 6 inches subtended by an angle of 113°Find the length of the radius, x, to the nearest tenth of an inch.

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

`\begin{gathered} Length\text{ of Arc = }(\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}`
`\begin{gathered} 6\text{ = }(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}`
`\begin{gathered} \text{x =}\frac{6\text{ x 360}}{113\text{ x 2 x }\pi} \\ x\text{ = }(2160)/(709.9999397) \end{gathered}`
`\begin{gathered} x\text{ = 3.042253779} \\ x\text{ }\approx\text{ 3.0 inches \lparen to the nearest tenth of an inch \rparen} \end{gathered}`

CONCLUSION:

The length of the radius, x, ( to the nearest tenth of an inch) = 3.0 inches