Euclidian Geometry Probability

chineseballer06 · 2011-02-01 05:39:30

Hey everyone, I have been working on this problem for a few days now and am just completely stuck. Im in college taking a probability and statistics course.

The problems is: A point is chosen at random inside a triangle with height h and base of length b. What is the probability that the perpendicular distance from the point to the baee is larger than d? What is the probability that the randomly chosen point and the base of the triangle will forma triangle with an obtuse angle when the original triangle is equilateral?

I need more help with the second part in setting up the problem because I think I can figure it out from there. All help is really appreciated. Thanks!

Oh and the answer is 1/2 + (pi/(6square root 3))

Last edited by chineseballer06 (2011-02-01 06:02:21)

Bob · 2011-02-01 10:03:44

hi chineseballer06

See diagram below.

The circle has BC as diameter.

When D is on the circle angle BDC = 90.

Inside the circle, it is obtuse and beyond the circle it is acute.

Hope that helps.

Or post again for more help.

Bob

Last edited by Bob (2011-02-01 10:11:22)

bobbym · 2011-02-01 15:45:13

Hi;

Laken · 2011-02-01 16:27:47

Does anyone know how to do the first part of the question? I am completely stuck on the first question and what d is supposed to be.

chineseballer06 · 2011-02-01 17:12:11

Okay thanks everyone that helps a lot!! And for the first part I think d is supposed to be the distance from that random point to the base, but yeah I agree the wording on the problem is confusing.

bobbym · 2011-02-01 20:24:13

Hi chineseballer06;

Do you have a solution for the first part or do you need one?

chineseballer06 · 2011-02-02 04:54:08

Yeah I do need one, I haven't figured it out yet. Thanks bobbym!

chineseballer06 · 2011-02-02 05:05:22

I think I have my picture right, I just don't understand what areas I am supposed to compute.

bobbym · 2011-02-02 05:05:39

Hi;

I do not have one yet either. I will post it as soon as I do.

chineseballer06 · 2011-02-02 05:09:08

the answer in the back of the book is (h-d)^2/(h^2)

but i don't know how they got that

Bob · 2011-02-02 05:30:11

hi chineseballer06

Sorry, I thought you had part 1 sorted.

See diagram below. The small triangle ADE and the larger one ABF, are similar.

Height ABF = h base ABF = b

Height ADE = h-d base ADE = b x (h-d)/h this being the scale factor for the (fractional) enlargement.

So the probability (being the ratio of the areas) will be

This simplifies to the answer you have.

Bob

Last edited by Bob (2011-02-02 05:30:54)

chineseballer06 · 2011-02-02 07:02:30

Thanks Bob! I appreciate it

bobbym · 2011-02-02 07:03:51

Oh, you got an answer. Hey, that is a nice one, Bob!!!!

Bob · 2011-02-02 07:20:51

hi chineseballer06

You are very welcome.

Thanks bobbym.

Bob

Math Is Fun Forum

#1 2011-02-01 05:39:30

Euclidian Geometry Probability

#2 2011-02-01 10:03:44

Re: Euclidian Geometry Probability

#3 2011-02-01 15:45:13

Re: Euclidian Geometry Probability

#4 2011-02-01 16:27:47

Re: Euclidian Geometry Probability

#5 2011-02-01 17:12:11

Re: Euclidian Geometry Probability

#6 2011-02-01 20:24:13

Re: Euclidian Geometry Probability

#7 2011-02-02 04:54:08

Re: Euclidian Geometry Probability

#8 2011-02-02 05:05:22

Re: Euclidian Geometry Probability

#9 2011-02-02 05:05:39

Re: Euclidian Geometry Probability

#10 2011-02-02 05:09:08

Re: Euclidian Geometry Probability

#11 2011-02-02 05:30:11

Re: Euclidian Geometry Probability

#12 2011-02-02 07:02:30

Re: Euclidian Geometry Probability

#13 2011-02-02 07:03:51

Re: Euclidian Geometry Probability

#14 2011-02-02 07:20:51

Re: Euclidian Geometry Probability

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