1. The problem asks to calculate $\tan^{-1}\left(\frac{r}{15}\right)$ for each given value of $r$.\n\n2. Recall that $\tan^{-1}(x)$, also called arctangent, is the inverse function of tangent, which returns an angle in radians whose tangent is $x$.\n\n3. For each $r$, compute the ratio $\frac{r}{15}$, then find the arctangent of that ratio.\n\n4. Calculations:\n- For $r=17.2$, $\frac{17.2}{15} = 1.1467$, $\tan^{-1}(1.1467) \approx 0.851$ radians\n- For $r=15.6$, $\frac{15.6}{15} = 1.04$, $\tan^{-1}(1.04) \approx 0.80$ radians\n- For $r=16.4$, $\frac{16.4}{15} = 1.0933$, $\tan^{-1}(1.0933) \approx 0.83$ radians\n- For $r=16.8$, $\frac{16.8}{15} = 1.12$, $\tan^{-1}(1.12) \approx 0.85$ radians\n- For $r=17.7$, $\frac{17.7}{15} = 1.18$, $\tan^{-1}(1.18) \approx 0.87$ radians\n- For $r=15.2$, $\frac{15.2}{15} = 1.0133$, $\tan^{-1}(1.0133) \approx 0.79$ radians\n- For $r=17.2$, same as above, $0.851$ radians\n- For $r=14.3$, $\frac{14.3}{15} = 0.9533$, $\tan^{-1}(0.9533) \approx 0.76$ radians\n- For $r=15.1$, $\frac{15.1}{15} = 1.0067$, $\tan^{-1}(1.0067) \approx 0.79$ radians\n- For $r=16.9$, $\frac{16.9}{15} = 1.1267$, $\tan^{-1}(1.1267) \approx 0.85$ radians\n- For $r=15.9$, $\frac{15.9}{15} = 1.06$, $\tan^{-1}(1.06) \approx 0.81$ radians\n- For $r=17.6$, $\frac{17.6}{15} = 1.1733$, $\tan^{-1}(1.1733) \approx 0.87$ radians\n- For $r=16.6$, $\frac{16.6}{15} = 1.1067$, $\tan^{-1}(1.1067) \approx 0.83$ radians\n- For $r=16.3$, $\frac{16.3}{15} = 1.0867$, $\tan^{-1}(1.0867) \approx 0.83$ radians\n- For $r=17.5$, $\frac{17.5}{15} = 1.1667$, $\tan^{-1}(1.1667) \approx 0.86$ radians\n- For $r=17.4$, $\frac{17.4}{15} = 1.16$, $\tan^{-1}(1.16) \approx 0.86$ radians\n- For $r=16.1$, $\frac{16.1}{15} = 1.0733$, $\tan^{-1}(1.0733) \approx 0.82$ radians\n- For $r=17.6$, same as above, $0.87$ radians\n- For $r=16.8$, same as above, $0.85$ radians\n- For $r=16.7$, $\frac{16.7}{15} = 1.1133$, $\tan^{-1}(1.1133) \approx 0.83$ radians\n\n5. These values are approximate and rounded to three decimal places.\n\nFinal answers (in radians):\n$[0.851, 0.80, 0.83, 0.85, 0.87, 0.79, 0.851, 0.76, 0.79, 0.85, 0.81, 0.87, 0.83, 0.83, 0.86, 0.86, 0.82, 0.87, 0.85, 0.83]$