1. **Problem statement:** A ladder of length 15 m leans against a vertical wall making an angle of 35° with the vertical wall. We need to find the height of the ladder above the ground. 2. **Formula and explanation:** In a right triangle, the height above the ground corresponds to the side adjacent to the angle between the ladder and the vertical wall. Since the ladder length is the hypotenuse, we use the cosine function: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ where $\theta = 35^\circ$, hypotenuse = 15 m. 3. **Calculate the height:** $$\cos(35^\circ) = \frac{\text{height}}{15}$$ Multiply both sides by 15: $$15 \times \cos(35^\circ) = \text{height}$$ 4. **Evaluate using a calculator:** $$\cos(35^\circ) \approx 0.8192$$ So, $$\text{height} = 15 \times 0.8192 = 12.288$$ 5. **Final answer:** The height of the ladder above the ground is approximately $$\boxed{12.3 \text{ meters}}$$ (correct to 1 decimal place).