Final Answer:
1. $\theta = \sin^{-1}\left(\frac{5}{13}\right)$ or $\theta \approx 22.6^\circ$
2. $\theta = \cos^{-1}\left(\frac{\sqrt{2}}{5}\right)$ or $\theta \approx 73.6^\circ$
3. $\theta = \tan^{-1}\left(\frac{8}{15}\right)$ or $\theta \approx 28.1^\circ$
4. $\theta = \tan^{-1}\left(\frac{3}{7}\right)$ or $\theta \approx 23.2^\circ$
5. $\theta = \tan^{-1}\left(\frac{4}{6}\right) = \tan^{-1}\left(\frac{2}{3}\right)$ or $\theta \approx 33.7^\circ$
6. $\theta = \sin^{-1}\left(\frac{27}{\sqrt{36^2 + 27^2}}\right) = \sin^{-1}\left(\frac{3}{5}\right)$ or $\theta = 36.9^\circ$
7. $\theta = \tan^{-1}\left(\frac{2}{\sqrt{15}}\right)$ or $\theta \approx 28.1^\circ$
8. $\theta = \cos^{-1}\left(\frac{4\sqrt{2}}{8}\right) = \cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = 45^\circ$
Parent Tip: Review the logic above to help your child master the concept of trigonometric ratios in right triangles worksheet.
