Given ladder length = 10 m and angle with ground = 45°. We are to determine the distance from the base of the ladder to the wall, which corresponds to the base BC in right triangle ABC. Applying the trigonometric relation for the base: \[ \cos 45^\circ = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{BC}{10} \] Consequently, \[ BC = 10 \times \cos 45^\circ = 10 \times \frac{1}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 5\sqrt{2} \text{ m} \]