Describe the Angular Size of an Arc Using Radians and Degrees

Question

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.

Answer 1

Hint:

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:

$$ \pi : 180°=x:\alpha^° $$