According to the recommended safety ratio of 4:1, how high will a 40-foot ladder reach when placed against a wall? Round to the nearest inch.

Answer 1

It will help you to do a quick sketch of a ladder leaning against a wall. The safety ratio of 4:1 means that for ever 1 foot away from the wall at ground level to the ladder base, you can gain 4 feet in height. You can solve this using the Pythagorean theorem. Draw a right triangle, with X at the base, and 4(x) for the height, and 40 for the hypotenuse. Now use Pythagorean Theorem:

1. X² + (4X)² = 40²
2. X² + 16X² = 1600
3. 17X² = 1600
4. X² = 94.11764
5. X = 9.701425
6. The height the ladder will reach is 4(x) = 38.8057'; rounded to the nearest inch = 38' 10" (pushing the safety limit by just a smidge)...

Answer 2

Set up a right triangle with base = x, height = 4x, and hypotenuse = 40 ft.

Use pythagorean theorem to solve for x:

a² + b² = c²

(base)² + (height)² = (hypotenuse)²

(x)² + (4x)² = (40)²

x² + 16x² = 1600

17x² = 1600

x² = 1600 / 17

x = √(1600 / 17) = 9.7 ft

height = 4x = 4(9.7) = 38.8 ft