I'm not sure about this. Am I right?

Question

173.The wheels on Devon’s bike have r-inch radii. After the front wheel picks up a tack,

Devon rolls another d feet and stops. How far above the ground is the tack?

Is the answer: r-r*cos(360*d/2*pi*r) ?

I've heard that it should be 12d instead of d. Why?

Answer 1

The answer of "12d" is definitely wrong because the correct answer must be

between 0 and 2r, no matter how large d gets.

You got it practically right. The answer is

r - r*cos(d/r)

You seemed to feel that the angle needs to be converted to degrees.

That is not the case.

The size of an angle is defined as the ratio between arc length and arc radius.

We just sometimes use degrees where it is more intuitive.

That little circle pronounced "degrees" is just shorthand for

° = 2π/360

For example,

90° = 90(2π/360) = π/2