Ladders problem
You have an alley with two walls, and resting against each wall are two ladders, which go from the either bottom corner to rest against either wall forming a diagonal cross.
If this doesnt make sense just google "ladder problem" and the diagrams are very simple.
The only values given are the height that each ladder touches a wall, one touching a 5m, the other at 10m. The aim is to find at what height do the two ladders cross.
This isnt like urgent homework or anything just something my brother was given as a challenge to test the way he thinks but not for him to actually solve, and I want to have a go
.
I would prefer for some ideas on working and how to go about it rather than telling me the answer straight up.
Thanks
If this doesnt make sense just google "ladder problem" and the diagrams are very simple.
The only values given are the height that each ladder touches a wall, one touching a 5m, the other at 10m. The aim is to find at what height do the two ladders cross.
This isnt like urgent homework or anything just something my brother was given as a challenge to test the way he thinks but not for him to actually solve, and I want to have a go
.I would prefer for some ideas on working and how to go about it rather than telling me the answer straight up.
Thanks
Original post by OKANEED
I would prefer for some ideas on working.
I would prefer for some ideas on working.
Couple of hints:
Similar triangles
A construction line. Spoilered as may be too big a hint, depending how your mind works.
Spoiler
Original post by OKANEED
...
Once you have solved that here is my version of the famous crossed ladder problem.
The original version of the problem usually leads to the use of numerical methods but my version has an EXACT solution that you can find without resorting to a calculator (admittedly there are plenty of surds):
Two ladders are placed across a narrow alleyway, so that the foot of each ladder rests against the bottom of one wall and the top of the ladder rests partway up the opposite wall.
One ladder is 2.6m long, and the other is 2.4m long. The ladders face opposite directions, making an X in the alleyway, with the intersection point 1m above the ground.
What is the EXACT width of the alleyway?
(edited 11 years ago)
Original post by Mr M
Once you have solved that here is my version of the famous crossed ladder problem.
The original version of the problem usually leads to the use of numerical methods but my version has an EXACT solution that you can find without resorting to a calculator (admittedly there are plenty of surds):
Two ladders are placed across a narrow alleyway, so that the foot of each ladder rests against the bottom of one wall and the top of the ladder rests partway up the opposite wall.
One ladder is 2.6m long, and the other is 2.4m long. The ladders face opposite directions, making an X in the alleyway, with the intersection point 1m above the ground.
What is the EXACT width of the alleyway?
The original version of the problem usually leads to the use of numerical methods but my version has an EXACT solution that you can find without resorting to a calculator (admittedly there are plenty of surds):
Two ladders are placed across a narrow alleyway, so that the foot of each ladder rests against the bottom of one wall and the top of the ladder rests partway up the opposite wall.
One ladder is 2.6m long, and the other is 2.4m long. The ladders face opposite directions, making an X in the alleyway, with the intersection point 1m above the ground.
What is the EXACT width of the alleyway?
i see what you mean
got to the last equation to solve for the width and just thought forget that...Original post by ghostwalker
Couple of hints:
Similar triangles
A construction line. Spoilered as may be too big a hint, depending how your mind works.
Similar triangles
A construction line. Spoilered as may be too big a hint, depending how your mind works.
Spoiler
Well my thought was to draw a line down from the intersection, creating two small triangles which are similar to the large triangles that contain them. The things in my head atm are to try and use pythagoras somewhere :s ive been fiddling around somewhat aimlessly and am wondering if this means anything:
Let the height of each wall equal X and Y and let the vertical from the intersection equal height V.
XY = V(X + Y)
A friend of mine saw this and mentioned a quartic equation? When I have a minute I am going to look it up, but is that relevant?
Original post by OKANEED
Well my thought was to draw a line down from the intersection, creating two small triangles which are similar to the large triangles that contain them. The things in my head atm are to try and use pythagoras somewhere :s ive been fiddling around somewhat aimlessly and am wondering if this means anything:
Let the height of each wall equal X and Y and let the vertical from the intersection equal height V.
XY = V(X + Y)
A friend of mine saw this and mentioned a quartic equation? When I have a minute I am going to look it up, but is that relevant?
Let the height of each wall equal X and Y and let the vertical from the intersection equal height V.
XY = V(X + Y)
A friend of mine saw this and mentioned a quartic equation? When I have a minute I am going to look it up, but is that relevant?
There is a quartic equation in my question but not in the original question. I'm not sure which one you are attempting!
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