1. **State the problem:** Solve the equation $$\cos(20) + x \sin(20) = 1$$ for $x$. 2. **Isolate $x$:** Subtract $\cos(20)$ from both sides: $$x \sin(20) = 1 - \cos(20)$$ 3. **Solve for $x$:** Divide both sides by $\sin(20)$: $$x = \frac{1 - \cos(20)}{\sin(20)}$$ 4. **Interpretation:** This expression gives the value of $x$ that satisfies the equation. 5. **Optional numerical approximation:** Using degrees, $$\cos(20) \approx 0.9397, \quad \sin(20) \approx 0.3420$$ So, $$x \approx \frac{1 - 0.9397}{0.3420} = \frac{0.0603}{0.3420} \approx 0.1763$$ **Final answer:** $$x = \frac{1 - \cos(20)}{\sin(20)} \approx 0.1763$$