1. **State the problem:** We have a right triangle formed by a pole leaning against a wall. The pole is the hypotenuse with length 15 m, and the distance from the wall to the foot of the pole is 10 m. We need to find the angle $x$ between the pole and the ground. 2. **Formula used:** In a right triangle, the cosine of the angle adjacent to the base is given by $$\cos x = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ Here, the adjacent side is the distance from the wall to the foot of the pole (10 m), and the hypotenuse is the pole length (15 m). 3. **Apply the formula:** $$\cos x = \frac{10}{15}$$ 4. **Simplify the fraction:** $$\cos x = \frac{\cancel{10}}{\cancel{15}} = \frac{2}{3}$$ 5. **Find the angle $x$ by taking the inverse cosine:** $$x = \cos^{-1}\left(\frac{2}{3}\right)$$ 6. **Calculate the value:** Using a calculator, $$x \approx 48.2^\circ$$ 7. **Final answer:** The angle the pole makes with the ground is approximately **48 degrees**.