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

Question

asked Dec 18, 2023 203k views

1 Answer

HiDayurie Dave · Answer 1 · 2023-12-21T18:35:36+0000

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