| View previous topic :: View next topic |
| Author |
Message |
perash
Guest
|
 Posted: Sun Jun 29, 2008 8:57 pm Post subject: Points A,B, and C |
 |
|
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to `. Determine the length CH such that \AHB is as large as possible. |
|
| Back to top |
|
 |
| |
Ads |
Advertising
Sponsor
|
|
perash
Guest
|
| Posted: Sun Jun 29, 2008 8:58 pm Post subject: Re: Points A,B, and C |
|
|
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to `. Determine the length CH such that <AHB is as large as possible. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
perash
Guest
|
| Posted: Sun Jun 29, 2008 9:05 pm Post subject: Re: Points A,B, and C |
|
|
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to BC. Determine the length CH such that < AHB is as large as possible. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
[Mr.] Lynn Kurtz
Guest
|
| Posted: Mon Jun 30, 2008 3:58 am Post subject: Re: Points A,B, and C |
|
|
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
| Quote: |
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to `. Determine the length CH such that \AHB is as large as possible.
|
OK, I got sqrt(10). What did you get?
--Lynn |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Virgil
Guest
|
| Posted: Mon Jun 30, 2008 6:27 am Post subject: Re: Points A,B, and C |
|
|
In article <MhRoSNgRk1Kq7oz8v1vzQQ3TL3Xd@4ax.com>,
"[Mr.] Lynn Kurtz" <kurtz@asu.edu.invalid> wrote:
| Quote: |
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2.
Point H is such that
CH is perpendicular to `. Determine the length CH such that \AHB is as large
as possible.
OK, I got sqrt(10). What did you get?
--Lynn
|
The same. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Virgil
Guest
|
| Posted: Mon Jun 30, 2008 11:00 am Post subject: Re: Points A,B, and C |
|
|
In article <Pine.BSI.4.58.0806292318550.8844@vista.hevanet.com>,
William Elliot <marsh@hevanet.remove.com> wrote:
| Quote: |
On Sun, 29 Jun 2008, [Mr.] Lynn Kurtz wrote:
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and BC
= 2. Point H is such that CH is perpendicular to `. Determine the
length CH such that \AHB is as large as possible.
You mean that the area of AHB is as large as possible?
OK, I got sqrt(10). What did you get?
That's there is no maximum.
|
As I read the problem, it was to find the length of CH needed to
maximize the angle AHB at point H, not the area of triangle ABH.
And I also found the maximizing length of CH to be sqrt(10) yielding an
angle at H of about .443 radians, or 25.4 degrees. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
William Elliot
Guest
|
| Posted: Mon Jun 30, 2008 11:00 am Post subject: Re: Points A,B, and C |
|
|
On Sun, 29 Jun 2008, [Mr.] Lynn Kurtz wrote:
| Quote: |
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and BC
= 2. Point H is such that CH is perpendicular to `. Determine the
length CH such that \AHB is as large as possible.
You mean that the area of AHB is as large as possible? |
| Quote: |
OK, I got sqrt(10). What did you get?
That's there is no maximum. |
|
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
William Elliot
Guest
|
| Posted: Mon Jun 30, 2008 11:00 am Post subject: Re: Points A,B, and C |
|
|
On Mon, 30 Jun 2008, Virgil wrote:
| Quote: |
William Elliot <marsh@hevanet.remove.com> wrote:
On Sun, 29 Jun 2008, [Mr.] Lynn Kurtz wrote:
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and
BC = 2. Point H is such that CH is perpendicular to `. Determine the
length CH such that \AHB is as large as possible.
You mean that the area of AHB is as large as possible?
OK, I got sqrt(10). What did you get?
That's there is no maximum.
As I read the problem, it was to find the length of CH needed to
maximize the angle AHB at point H, not the area of triangle ABH.
That makes sense. |
| Quote: |
And I also found the maximizing length of CH to be sqrt(10) yielding an
angle at H of about .443 radians, or 25.4 degrees.
Ok, so do I using the formula for the |
tangent of the difference of two angles.
---- |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Virgil
Guest
|
| Posted: Tue Jul 01, 2008 12:58 am Post subject: Re: Points A,B, and C |
|
|
In article <20080629235956.D9658@agora.rdrop.com>,
William Elliot <marsh@rdrop.remove.com> wrote:
| Quote: |
On Mon, 30 Jun 2008, Virgil wrote:
William Elliot <marsh@hevanet.remove.com> wrote:
On Sun, 29 Jun 2008, [Mr.] Lynn Kurtz wrote:
On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and
BC = 2. Point H is such that CH is perpendicular to `. Determine the
length CH such that \AHB is as large as possible.
You mean that the area of AHB is as large as possible?
OK, I got sqrt(10). What did you get?
That's there is no maximum.
As I read the problem, it was to find the length of CH needed to
maximize the angle AHB at point H, not the area of triangle ABH.
That makes sense.
And I also found the maximizing length of CH to be sqrt(10) yielding an
angle at H of about .443 radians, or 25.4 degrees.
Ok, so do I using the formula for the
tangent of the difference of two angles.
|
I used the law of cosines, myself, and incidentally discovered that the
maximum angle subtended by AB at H always occurs when CH is the mean
proportional of AC and BC:
AC/CH = CH/BC or CH^2 = AC*BC |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Barry Schwarz
Guest
|
| Posted: Tue Jul 01, 2008 5:30 am Post subject: Re: Points A,B, and C |
|
|
On Sun, 29 Jun 2008 17:05:02 EDT, perash <mk_917@hotmail.com> wrote:
| Quote: |
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to BC. Determine the length CH such that < AHB is as large as possible.
|
It is sufficient to find the maximum of tan(AHB).
tan(AHB) = tan(AHC - BHC)
Using the standard trig formula for the tangent of a difference plus
what you know about the tangents of AHC and BHC, you should be able to
take it from here.
Remove del for email |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
hagman
Guest
|
| Posted: Wed Jul 02, 2008 3:54 pm Post subject: Re: Points A,B, and C |
|
|
On 29 Jun., 22:57, perash <mk_...@hotmail.com> wrote:
| Quote: |
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2. Point H is such that
CH is perpendicular to `. Determine the length CH such that \AHB is as large as possible.
|
This is the famous mini-skirt problem, isn't it?
The angle is maximal when the line CH is tangent to the circumscribed
circle of triangle ABH. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
Virgil
Guest
|
| Posted: Wed Jul 02, 2008 10:18 pm Post subject: Re: Points A,B, and C |
|
|
In article
<e3992405-2c65-4725-9fe4-76736eb56ca5@l64g2000hse.googlegroups.com>,
hagman <google@von-eitzen.de> wrote:
| Quote: |
On 29 Jun., 22:57, perash <mk_...@hotmail.com> wrote:
Points A,B, and C lie in that order on line `, such that AB = 3 and BC = 2.
Point H is such that
CH is perpendicular to `. Determine the length CH such that \AHB is as
large as possible.
This is the famous mini-skirt problem, isn't it?
The angle is maximal when the line CH is tangent to the circumscribed
circle of triangle ABH.
|
More simply, CH is the mean proportional of AC and BC. |
|
| Back to top |
|
|
| |
Ads |
Advertising
Sponsor
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
199 Attacks blocked
Powered by phpBB © 2001, 2005 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
