Re: Points A,B, and C

On Mon, 30 Jun 2008, Virgil wrote:
> William Elliot <marsh@[EMAIL PROTECTED]
> wrote:
>> On Sun, 29 Jun 2008, [Mr.] Lynn Kurtz wrote:
>>> On Sun, 29 Jun 2008 16:57:03 EDT, perash <mk_917@[EMAIL PROTECTED]
> 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.

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