Question

a right triangle form by ladder against a wall the ladder is 20 feet, and top of the ladder rests 19 ft up in the height of the wall find the approvximate angle form where the top where the of the ladder rests against the wall

Answer 1

Let the ladder (20 ft) be the hypotenuse and the wall height be the vertical leg (19 ft). The angle at the top (between the ladder and the wall) is the acute complement of the angle the ladder makes with the ground.

Compute the horizontal distance: base = sqrt(20^2 − 19^2) = sqrt(39) ≈ 6.245 ft.

Angle at the top = arcsin(base / ladder) = arcsin(√39 / 20) ≈ arcsin(0.31225) ≈ 18.2°.

(Equivalently, the angle between ladder and ground = arcsin(19/20) ≈ 71.8°.)