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#1 2019-08-25 22:50:38

ashraf
Guest

by using vectors

how to prove that a squared = b squared + c squared - 2 b c cos A in any triangle

#2 2019-08-27 00:10:37

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: by using vectors

hi ashraf

Welcome to the forum.

It comes directly from the dot or scalar product.

https://www.mathsisfun.com/algebra/vect … oduct.html

so

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2019-08-28 01:54:21

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: by using vectors

make up a straight triangle with angle A and line c and you can arrive at this equation:

aa - (b-cCosA)^2 = cSinASinA

using Gougu theorem.

This equation is equivalent to the theorem you mentioned.


X'(y-Xβ)=0

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#4 2019-08-28 02:02:46

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: by using vectors

If A > pi/2 however, CosA = - Cos(pi-A)
Make up the angle Cos(pi-A) by extending b or c until you form a straight triangle with C or B and a
You then have a bigger straight triangle and a smaller one sharing the same straight line which can be calculated using SinA
Samiliar calculation goes and you will arrive at the same equation.


X'(y-Xβ)=0

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