Hello all. I’ve just started my first semester in Calculus and Analytic Geometry, and it’s been going rather rough. While I enjoy doing math, I just can’t seem to grasp all the rules and tricks to solve for some of these problems. So, a few days ago, our teacher gave us a story problem, to guage how well we can handle more involved, lengthy steps. He’s allowed anyone to stop by for help with their assignment, which I’ve done, but I still can’t figure out how to solve this problem in any way. I was hoping some smart math dopers could at least point me in the right direction.
Problem: We have an 8 foot high fence which seperates a clear area and a building. The building’s height is unimportant. The distance from the wall and the building is 4 feet. The goal is to place a ladder on the opposite side of the wall and lean it up against the building, obviously in such a way that it clears the 8 foot high fence. The shortest length of ladder to clear the wall and touch the building is the answer.
In drawing a picture, I get two triangles. One that connects the base of the ladder to the wall (I’m assuming the shortest possible ladder would just touch the wall) and one that goes from the base of the wall to the building. The one at the building would have a width of 4, and would be 8 feet high. I draw an inverse triangle that went down to the base of the building, instead of going up, thus giving me a triangle with two known sides (8 feet high, 4 feet wide). I figure distances would be the same for the hypotenuse of the triangle in either direction (may be wrong on that). Pictures would help, here.
I solved and had 8.944 ft. as the length of the hypotenuse of the second triangle. My triangle that connects from the ground to the wall is still unknown, and I don’t know what to do with it. Everything is unknown (as far as I know) except it’s height (8 feet). How do I figure the first triangles hypotenuse length or the angle and manage (I.E. get lucky) to find the length of the shortest possible ladder that can touch the building?