Feet per radian to feet per degrees?

Question

How can we convert feet/radian to feet/degrees?

I need to convert $-7600\sqrt 3 \frac{feet}{radians}$

I know the answer is:

$-\frac{380 \pi} {9} \sqrt 3$

=$-230$ $\frac{feet}{degrees}$ approx

But i don t understand how.

Any help will be appreciated!

Answer 1

Both the use of degrees and radians are measurements of angles. And both are utterly arbitrary. There are 360 degrees in a circle. There are 2$\pi$ radians in a circle.

Therefore:

1 degree = $\frac {2\pi}{360} = \frac {\pi}{180}$ radians.

And

1 radian = $\frac {360}{2\pi} = \frac {180}{\pi}$ degrees.

So $ -7600*(3)^{1/2} \text{feet}/\text{radians} = -7600*(3)^{1/2} \text{feet}/\text{radians} \cdot \frac{2 \pi \text{ radians}}{360\text {degree}}= -2\pi\cdot \frac{7600}{360}\cdot 3^{1/2}\frac{\text{feet}}{\text{degrees}}= \sqrt{3}\cdot\pi \frac {380}{9} \frac{\text{feet}}{\text{degrees}}$

Answer 2

$$\frac{-7600\sqrt{3}\text{ feet}}{1 \text{ radian}}\cdot\frac{2\pi\text{ radians}}{360\text{ degrees}} = ?$$ Hint: the radian units cancel out, leaving you with $\frac{feet}{degree}$.