My post of The importance of visualization elicited the following response:
Hi Scott Sheppard,
[email protected] has left you a comment:
The correct answer is 4 feet. It's a trick question. Has nothing to do with Pythagorean theorem. You have a fixed length object and a 90-degree angle. Everything else is irrelevant info thrown in to confuse. Draw it up in AutoCAD :)
For those who didn't see the question in my original post:
A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out how many feet?
According The Official SAT Question of the Day site, my answer of 8 feet was correct:
The ladder, the wall, and the ground form a right triangle with a 25-foot hypotenuse. At first, the bottom of the ladder is 7 feet from the base of the building, so one leg of the right triangle measures 7 feet; the length of the other leg, x, can be found by solving 72 + x2 = 252, which is the Pythagorean theorem. From this, you can figure out that the other leg measures 24 feet.
After the ladder slips down 4 feet, the 24-foot leg of the right triangle becomes 20 feet long. The other leg then has to be 15 feet long. This length is found by solving 202 + y2 = 252, which is again the Pythagorean theorem.
Since the distance between the bottom of the ladder and the base of the building increases from 7 feet to 15 feet, the amount that the bottom of the ladder slides out is 8 feet.
Despite the fact that my original answer was correct using the Pythagorean theorem, I liked [email protected]'s suggestion of drawing it up in AutoCAD.
Thanks to Heidi Hewett for the tip regarding setting my dynamic input to use absolute coordinates.
Using design applications to check the math is alive in the lab.