If I have the triangle ABC, that A(3,4) B(1,2) C(6,1)

How can I find the value of angle A? :confused:

Please, thank you

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- January 27th 2007, 11:12 PMsallsavector please.....
If I have the triangle ABC, that A(3,4) B(1,2) C(6,1)

How can I find the value of angle A? :confused:

Please, thank you - January 28th 2007, 12:16 AMearboth
Hello,

from the title of your post I assume that you have to use vectors (If you don't want to use vectors you can solve this problem by using Cosine rule)

1. Calculation of the vectors:

2. The angle between 2 vectors and is calculated by:

Plug in the vectors you know into this formula:

Therefore A = 90° : You are dealing with a right triangle.

3. Hint: Draw a sketch of this triangle to prove the calculations.

EB - January 28th 2007, 12:17 AMCaptainBlack
Calculate the squares of the lengths of the sides:

AB^2=(3-1)^2+(4-2)^2=8

AC^2=(3-6)^2+(4-1)^2=18

BC^2=(1-6)^2+(2-1)^2=26.

So AB^2+AC^2=BC^2. Therefore by the converse of Pythagoras's theorem

ABC is a right triangle with BC as hypotenuse, and the angle at A is a right

angle.

RonL