1. **State the problem:** We have a right triangle with angle $A = 39^\circ$, right angle at $B$, and side $BC = 2$. We need to find side $AC = x$. 2. **Identify the sides relative to angle $A$:** - Side $BC = 2$ is adjacent to angle $A$. - Side $AC = x$ is opposite angle $A$. 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{2}$$ 4. **Solve for $x$:** $$x = 2 \times \tan(39^\circ)$$ 5. **Calculate $\tan(39^\circ)$:** Using a calculator, $\tan(39^\circ) \approx 0.8098$ 6. **Find $x$:** $$x = 2 \times 0.8098 = 1.6196$$ 7. **Round to the nearest hundredth:** $$x \approx 1.62$$ **Final answer:** $x = 1.62$