1. **State the problem:** We need to find the length of side $x = MN$ in a right triangle $MNO$ where the right angle is at $N$, side $NO = 7$, and angle $O = 52^\circ$. 2. **Identify the sides relative to angle $O$:** - Side $NO = 7$ is adjacent to angle $O$. - Side $MN = x$ is opposite angle $O$. 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: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Set up the equation:** $$\tan(52^\circ) = \frac{x}{7}$$ 5. **Solve for $x$:** Multiply both sides by 7: $$7 \times \tan(52^\circ) = x$$ 6. **Calculate the value:** $$x = 7 \times \tan(52^\circ)$$ Using a calculator: $$\tan(52^\circ) \approx 1.2799$$ So, $$x \approx 7 \times 1.2799 = 8.9593$$ 7. **Round to the nearest tenth:** $$x \approx 9.0$$ **Final answer:** $$\boxed{9.0}$$