Question

How do I turn the degree into a radian and solve the problem

Answer 1

Step by step explanation:

To turn degrees into radian yuo have to multiply for the conversion factor, remember that pi radians are equal to 180 degrees, so:

`75^o=75^o\cdot\frac{\pi\text{ rad}}{180^o}=(5\pi)/(12)\text{rad}`

And for the problem we can first find the total area, if 75° is 12cm^2. How much do 360° correspond to?

`\begin{gathered} (A)/(360)=(12)/(75) \\ A=(12\cdot360)/(75) \\ A=57.6cm^2 \end{gathered}`

Now we can use the area formula:

`A=\pi\cdot r^2`
`57.6=\pi\cdot r^2`
`(57.6)/(\pi)=r^2`
`r=\sqrt[]{(57.6)/(\pi)}`
`r\approx4.3cm`

The radius is approximately 4.3 cm