The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?

$6\sqrt{2}$ m

⇒ cos \({45}^\circ\) = \(\frac{BC}{12}\)

⇒ \(\frac{1}{√2}\) = \(\frac{BC}{12}\)

⇒ BC = \(\frac{12}{√2}\) = 6\(\sqrt {2 }\)m.

Therefore, the distance between the wall and the foot of the ladder is 6\(\sqrt {2 }\)m.