1. **State the problem:** We have a right triangle NML with a right angle at M. Angle N is 46° and side NL (opposite angle M) is 4.1 units. We need to find side NM (adjacent to angle N), labeled as $x$. 2. **Identify the trigonometric relationship:** Since we know the angle and the side opposite to it, and want to find the adjacent side, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 46^\circ$, opposite side = 4.1, adjacent side = $x$. 3. **Set up the equation:** $$\tan(46^\circ) = \frac{4.1}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\tan(46^\circ)$: $$x \times \tan(46^\circ) = 4.1$$ $$x = \frac{4.1}{\tan(46^\circ)}$$ 5. **Calculate the value:** $$\tan(46^\circ) \approx 1.0355$$ $$x = \frac{4.1}{1.0355}$$ 6. **Simplify and round:** $$x \approx 3.96$$ Rounded to the nearest tenth: $$x \approx 4.0$$ **Final answer:** $$x = 4.0$$