I was going to use law of cosines at first, until it struck me that the Pythagorus Theorem solved this one much more elegantly and simply.
For those suggesting this needs more information, what reason do you have to think there are complicating factors in what amounts to a trigonometry word problem?
I understand how this might be much more complicated as an engineering-level problem, where you cannot make simplifying assumptions, and thus require more detailed information, but nothing in the problem indicates it is intended to have that level of complexity, and in fact, the poser of the problem gave indication that basic common sense assumptions would suffice.
1) Roots are on the pond bed, not free-floating.
2) Stem remains taut and straight at all times.
These are sufficient to give you a basic answer with a touch of trig and algebra.
Originally posted by geepamoogleSo insufficient information is correct geep, or you wouldn't have had to modify the problem 😉 why don't you be a man and just admit it. All plants don't grow the same, you are just twisting the problem definition after the fact. The only thing a reasonable person can assume is that the pond is at least 5 feet deep and nothing more.
I was going to use law of cosines at first, until it struck me that the Pythagorus Theorem solved this one much more elegantly and simply.
For those suggesting this needs more information, what reason do you have to think there are complicating factors in what amounts to a trigonometry word problem?
I understand how this might be much more complica ...[text shortened]... all times.
These are sufficient to give you a basic answer with a touch of trig and algebra.
Originally posted by eldragonflyPlease reword the question so that all required information is provided.
So insufficient information is correct geep, or you wouldn't have had to modify the problem 😉 why don't you be a man and just admit it. All plants don't grow the same, you are just twisting the problem definition after the fact. The only thing a reasonable person can assume is that the pond is at least 5 feet deep and nothing more.
Originally posted by PBE6Ok, I see his point.
Please reword the question so that all required information is provided.
A woman walks by a pond, and sees a beautiful flower growing on a stem in the middle of the pond. The stem is rooted in the bottom of the pond. She finds a 5 foot stick by the pond, which just allows her to reach the flower and drag to the edge, where the flower just touches the water. She then picks the flower with 1 foot of the stem attached, and lets the rest float back to the centre of the pond. She notes that the freshly cut stem now just barely crests the top of the water.
How deep is the pond?
Originally posted by AThousandYoungWrong.
Ok, I see his point.
A woman walks by a pond, and sees a beautiful flower growing on a stem in the middle of the pond. [b]The stem is rooted in the bottom of the pond. She finds a 5 foot stick by the pond, which just allows her to reach the flower and drag to the edge, where the flower just touches the water. She then picks the flower with 1 ...[text shortened]... the freshly cut stem now just barely crests the top of the water.
How deep is the pond?[/b]
Originally posted by eldragonflyDo you ever pump the bishop when posting? I only ask because it seems like the blood rushes out of your head every time you sit down to type.
Uh huh. Yet another silly "cut and paste" word problem from PBE6, who can never explain what he meant or adequately describe the problem. You should run for office or something my man.
Originally posted by PBE6Just answer the question, why should i assume that the lake is more than 1 foot deep, that's the flower + the one foot stem? Fact is this is another silly word problem, not very insightful. If you would be so kind PBE6 since i'm willing to let by-gones be by-gones, please pm me the solution. i just want to see the math, i promise i won't criticize the reasoning or lack thereof behind it.
Do you ever pump the bishop when posting? I only ask because it seems like the blood rushes out of your head every time you sit down to type.
Originally posted by PBE6ad hominem=logical fallacy. pm me the solution, i want to see where this goes PBE6, nevermind the modified problem statement by geep.
@ATY: Lol, I guess he didn't see yours. 🙄
eldragonfly amuses me to no end. One of these days, he's going to a veritable "Gallagher" on the world comic stage.
Originally posted by eldragonflyNo need for a pm, spanky, just refer to the following un-edited posts:
Just answer the question, why should i assume that the lake is more than 1 foot deep, that's the flower + the one foot stem? Fact is this is another silly word problem, not very insightful. If you would be so kind PBE6 since i'm willing to let by-gones be by-gones, please pm me the solution. i just want to see the math, i promise i won't criticize the reasoning or lack thereof behind it.
#1 "A woman walks by a pond, and sees a beautiful flower growing on a stem in the middle of the pond. She finds a 5 foot stick by the pond, which just allows her to reach the flower and drag to the edge, where the flower just touches the water. She then picks the flower with 1 foot of the stem attached, and lets the rest float back to the centre of the pond. She notes that the freshly cut stem now just barely crests the top of the water.
How deep is the pond?"
*****
#2 "Nope, but I should clarify the wording in the problem.
The distance from the edge of the pond to the flower is 5 feet, and the flower sticks out 1 foot above the surface of the water before being cut. You can assume that the flower stem is taught and remains a straight line from the flower to the centre-bottom of the pond at all times."
*****
Let the original length of the flower stem be R. The length from the edge of the pond to the flower is 5 feet, and 1 foot is plucked from the stem by the lady, leaving the stem R-1 feet long. This is the depth of the pond since the stem now only barely crests the water when returned to its original position. Since the flower just touched the water when dragged to the edge of the pond, we know that the length from the edge of the pond to the centre-bottom is R.
Now, we have a right angle triangle with R as the hypotenuse, 5 as one leg and R-1 as the other. By the Pythagorean theorem, we have:
R^2 = (R-1)^2 + 5^2
R^2 = R^2 - 2R + 1 + 25
2R = 26
R = 13
Since R-1 is the depth, the answer to the question is:
R-1 = 13 - 1 = 12.
1 edit
Now, we have a right angle triangle with R as the hypotenuse, 5 as one leg and R-1 as the other. By the Pythagorean theorem, we have:Thanks, but R could be 1 making the use of the pythagorean theorem impossible. And R is not the hypotenuse, the imaginary distance from the edge of the pond to the bottom of the pond is. So your problem is poorly structured for many reasons..
R^2 = (R-1)^2 + 5^2
R^2 = R^2 - 2R + 1 + 25
2R = 26
R = 13
Since R-1 is the depth, the answer to the question is:
R-1 = 13 - 1 = 12.[/b]
"Let the original length of the flower stem be R."
which also happens to be the depth of the pond therefore this is a direct contradiction to this faulty assumption:
"Since R-1 is the depth,"
Here i'll say it one more time :
Insufficient information. 😕