A Ladder Against a Wall

A ladder against a wall makes a right triangle: the wall and the ground meet at the right angle, and the ladder is the hypotenuse. Safety guides ask for about 75° between the ladder and the ground.

A 5 m ladder stands at 70°. How far is its foot from the wall? That distance d touches the 70° angle at the foot, so it is adjacent, and the ladder is the hypotenuse: $\cos\left(70^{\circ}\right) = \frac{d}{5}$, so $d = 5\cos\left(70^{\circ}\right)$, about 1.71 m. The height it reaches is opposite 70°, so it needs the sine instead.