A classic right triangle: wall height, ground distance, ladder as hypotenuse.
Key formulas
Identify sides
The wall and ground meet at 90°. The ladder is the hypotenuse whether or not the diagram looks steep.
Example
Base 3 m, wall 4 m → ladder 5 m. Angle with ground: tan⁻¹(4/3).
Sliding ladder
Related rates versions appear later; at secondary level, freeze one moment and apply Pythagoras.
Worked example
Worked example
Problem. A ladder is 10 m long and its foot is 6 m from a vertical wall. How high up the wall does it reach?
Solution. Height = √(10² − 6²) = √(100 − 36) = √64 = 8 m.
Safety angle
Some questions require the angle with the ground to exceed a given value.
Review quiz
Ladder 13 m, reaches 12 m up the wall. Distance from wall to foot is:
Practice questions
- Ladder 10 m, base 6 m. How high up the wall?
- Find the angle with the ground in the 3-4-5 ladder.
Study notes
Does the wall have to be vertical?
School problems assume it is, unless stated otherwise.