1. **Problem Statement:** Find the value of angle $\theta$ in a right triangle where the side opposite to $\theta$ is 11.9 and the side adjacent to $\theta$ is 10. 2. **Trig Ratio Selection:** Since we know the opposite and adjacent sides, we use the tangent ratio: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(\theta) = \frac{11.9}{10}$$ 4. **Calculate the ratio:** $$\tan(\theta) = 1.19$$ 5. **Find the angle $\theta$ by taking the arctangent:** $$\theta = \tan^{-1}(1.19)$$ 6. **Evaluate using a calculator:** $$\theta \approx 50.2^\circ$$ 7. **Round to the nearest whole number:** $$\theta \approx 50^\circ$$ **Final answer:** $$\theta = 50^\circ$$ **Trig Ratio Used:** Tangent (tan)