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#1 2013-07-06 04:07:32

mukesh
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solution of triangle

if the median 'AD' of a triangle 'ABC' is perpendicular to side AB then prove that    'tanA+2tanB=0'

#2 2013-07-06 23:25:05

bob bundy
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Re: solution of triangle

hi mukesh,

Here's an outline of a way to prove this.  see diagram below.



There's no right angle to get tanA easily so I used the sine and cosine rules:



and



Put these together to get tanA and simplify.

work on this expression for tanA, making use of the following:









After much simplification you can get this equal to -2tanB, from which the required result follows.

It's a tough one so expect it to take 2 or 3 pages.  If you get stuck post back where you've got to, and I'll compare your answer with mine.

Bob


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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#3 2013-07-06 23:33:08

anonimnystefy
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Re: solution of triangle

Well, I have a solution that takes 2 or 3 lines to write up, but requires quite a bit of inspection.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#4 2013-07-07 01:05:22

bob bundy
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Re: solution of triangle

hi Stefy,

What does 'quite a bit of inspection' mean exactly.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#5 2013-07-07 01:44:24

anonimnystefy
Real Member

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Re: solution of triangle

I do not have an exact definition. Roughly, it means that some times you will think of it, sometimes you won't, and it mostly depends on luck, not unlike many other geometry problems.

My solution extends the line AB and names E the foot of the perpendicular from C to that line. Then I used The basic trig equations to get the result.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#6 2013-07-07 02:45:27

bob bundy
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Re: solution of triangle

hi Stefy,

That is a brilliant way to do it.  Short and no complicated trig stuff.  I am in awe.  smile smile smile ( no dazzled-smiley-face available)

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#7 2013-07-07 02:52:18

anonimnystefy
Real Member

Online

Re: solution of triangle

The thing I dislike about those kinds of ideas are that they can be tough to get. It does come down to luck and experience a lot.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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