1. **State the problem:** We have a triangle split into two right triangles by a vertical height. The left triangle has an angle of 54° and a base of 8.2 cm. The right triangle has an angle of 36° and a base of length $x$. We need to find $x$. 2. **Identify the shared height:** Let the height be $h$. Both right triangles share this height. 3. **Use trigonometry on the left triangle:** The angle is 54°, adjacent side is 8.2 cm, opposite side is $h$. Using tangent: $$\tan(54^\circ) = \frac{h}{8.2}$$ So, $$h = 8.2 \times \tan(54^\circ)$$ 4. **Calculate $h$:** $$h = 8.2 \times 1.37638 = 11.28 \text{ cm (approx)}$$ 5. **Use trigonometry on the right triangle:** The angle is 36°, opposite side is $h$, adjacent side is $x$. Using tangent: $$\tan(36^\circ) = \frac{h}{x}$$ Rearranged: $$x = \frac{h}{\tan(36^\circ)}$$ 6. **Substitute $h$ and calculate $x$:** $$x = \frac{11.28}{0.72654} = 15.53 \text{ cm (approx)}$$ 7. **Round to 1 decimal place:** $$x = 15.5 \text{ cm}$$ **Final answer:** $$\boxed{15.5 \text{ cm}}$$