A triangle has sides A, B, and C. Sides A and B are of lengths $8$ and $1$ , respectively, and the angle between A and B is $pi/3$ . What is the length of side C?

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Answer 1 · 2016-06-27T04:45:02

$C=sqrt57$

By the Carnot theorem, you know that:

$C^2=A^2+B^2-2ABcosgamma$

Since $A=8, B=1 and gamma=pi/3$ :

$C=sqrt(8^2+1^2-2*8*1*cos(pi/3))$

$C=sqrt(65-16*1/2)$

$C=sqrt57$

A triangle has sides A, B, and C. Sides A and B are of lengths 88 and 11, respectively, and the angle between A and B is pi/3pi/3. What is the length of side C?