What is the law of cosines?

1 Answer
Gió
Dec 21, 2014

Cosider the triangle:

enter image source here
(Picture source: Wikipedia)

you can relate the sides of this triangle in a kind of "extended" form of Pitagora's Theorem giving:

#a^2=b^2+c^2-2bc*cos(alpha)#
#b^2=a^2+c^2-2ac*cos(beta)#
#c^2=a^2+b^2-2ab*cos(gamma)#

As you can see you use this law when your triangle is not a right-angled one.

Example:
Consider the above triangle in which:
#a=8 cm#
#c=10 cm#
#beta=60°# therefore:
#b^2=a^2+c^2-2ac*cos(beta)#
#b^2=8^2+10^2-2*8*10*cos(60°)# but #cos(60°)=1/2#
so: #b^2=84 and b=sqrt(84)= 9,2 cm#

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