Tracy D. answered • 10/08/20

Upbeat, patient Math Tutor investing in students to succeed

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:

- X
^{2}+ (4X)^{2}= 40^{2} - X
^{2}+ 16X^{2 }= 1600 - 17X
^{2}= 1600 - X
^{2}= 94.11764 - X = 9.701425
- 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)...