Question

How would I find the measure of the central angle ? What should I start with ?

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

`\begin{gathered} Arc\text{ length =}(\theta)/(360^0)\text{ x 2}\pi\text{ r} \\ where\text{ arc length = 4 units} \\ and\text{ the radius, r = 3 units} \end{gathered}`
`\begin{gathered} puttin\text{g the values, we have that:} \\ \text{4 =}(\theta)/(360^0)\text{ x 2 x }\pi\text{ x 3} \\ Then,\text{ we have that:} \end{gathered}`
`\begin{gathered} cross\text{ - multiply, we have that:} \\ 4\text{ x 360}^0\text{ = }\theta\text{ x 6}\pi \\ 1440^0\text{ = }\theta\text{ x 6}\pi \end{gathered}`
`\begin{gathered} Divide\text{ both sides by 6}\pi\text{, we have that:} \\ \theta\text{ =}(1440^0)/(6\pi)=(240)/(\pi) \end{gathered}`
`\begin{gathered} Note\text{ that:} \\ 2\pi\text{ }rad\text{ = 360}^0 \end{gathered}`
`\begin{gathered} 2\pi rad\text{ = 360}^0 \\ ?\text{ = }(240)/(\pi)=\text{ 76}(4)/(11)\text{ }^0\text{ = }(840^0)/(11^) \end{gathered}`
`?\text{ =}\frac{2\pi\text{ rad x }(840)/(11)}{360}`
`?\text{ = }\frac{\pi\text{ rad}}{180}\text{ x }(840)/(11)`
`?\text{ =}(14)/(33)\text{ }\pi\text{ rad }\approx\text{ 0.42 }\pi\text{ rad \lparen correct to 2 decimal places\rparen}`

CONCLUSION:

The measure of the central angle ( in radians) =

`0.42\pi\text{ \lparen correct to 2 decimal places\rparen}`