Question

explore radian measure by following these steps. and radius arc length = ∠ × radius √ 3. because all circles are similar, for any circle with radius r and arc length s, there is a constant of proportionality k, such that r = k × 1. it is also true that for any central angle θ, s = k × θ √. 4. therefore by substitution, s =

Explanation:

Step1: Recall arc - length formula

The formula for the arc - length $s$ of a circle with radius $r$ and central angle $\theta$ (in radians) is $s = r\theta$.

Step2: Analyze given relationships

We know from the problem that $r = k\times1$ and $s=k\times\theta$. Substituting $k = r$ into the second equation $s = k\times\theta$, we get $s=r\theta$.

Answer:

$r\theta$