Math Is Fun Forum

ashraf

Guest

by using vectors

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

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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

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.

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X'(y-Xβ)=0

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.

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X'(y-Xβ)=0