1. **State the problem:** We have a right triangle formed by points A, B, C, and D with a zip wire AC as the hypotenuse. Given CD = 2.6 m, BD = 12 m, and BC calculated as $\sqrt{12^2 + 2.6^2} = 12.2$ m, we want to find the angle $x$ between the zip wire AC and the horizontal line AB, where $x \geq 5^\circ$. 2. **Identify the triangle and sides:** The triangle ABC is right-angled at B. We know BC = 12.2 m (hypotenuse), BD = 12 m (horizontal base), and CD = 2.6 m (vertical height). The angle $x$ is at point A between AB (vertical) and AC (zip wire). 3. **Use trigonometric ratios:** To find angle $x$, use the tangent function which relates the opposite side to the adjacent side in a right triangle: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{CD}{BD} = \frac{2.6}{12}$$ 4. **Calculate the angle $x$:** $$x = \tan^{-1}\left(\frac{2.6}{12}\right)$$ Calculate the value: $$x = \tan^{-1}(0.2167) \approx 12.3^\circ$$ 5. **Interpret the result:** The angle $x$ is approximately $12.3^\circ$, which satisfies the condition $x \geq 5^\circ$. **Final answer:** $$x \approx 12.3^\circ$$