The question is as follows:

A 6-inch arc is drawn using a 4-inch radius. Describe the angular size of the arc (a) using radians; (b) using degrees.

I did the following to find the central angle of the circle that would create an arc of 6 inches.

$$ 2\pi (4)(\frac{x}{360}) = 6$$

From this equation, I found the value of $x$ to be $\approx 85.944$. I know that it would take $360 \div 85.944$ (which is $\approx 4.189$) arcs of 6 inches to fill the circumference of the circle. I don't know how to put this number into radians or is $4.189$ already in radians and $85.944$ already in degrees?

Any help will be greatly appreciated.



The radians measure of an arc is, by definition,

the length of the arc divided by the radius of the circle.

And, if $x$ is the radians measure, the corresponding measure in degrees $\alpha^°$ is given by:

$$ \pi : 180°=x:\alpha^° $$


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