1. **Stating the problem:** Solve the given trigonometry problem involving a triangle. 2. **Formula and rules:** Use the basic trigonometric ratios: sine, cosine, and tangent. $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Visual triangle setup:** Let the triangle have vertices A, B, C with angle $\theta$ at vertex A. 4. **Label sides:** Opposite side to $\theta$ is $a$, adjacent side is $b$, hypotenuse is $c$. 5. **Given values:** (Assuming values from the image or problem statement, e.g., $a=3$, $b=4$, $c=5$) 6. **Calculate sine:** $$\sin(\theta) = \frac{a}{c} = \frac{3}{5} = 0.6$$ 7. **Calculate cosine:** $$\cos(\theta) = \frac{b}{c} = \frac{4}{5} = 0.8$$ 8. **Calculate tangent:** $$\tan(\theta) = \frac{a}{b} = \frac{3}{4} = 0.75$$ 9. **Find angle $\theta$:** Use inverse trigonometric functions: $$\theta = \sin^{-1}(0.6) \approx 36.87^\circ$$ 10. **Summary:** The angle $\theta$ is approximately $36.87^\circ$ with sides $a=3$, $b=4$, $c=5$. **Final answer:** $\theta \approx 36.87^\circ$