A triangle has sides A, B, and C. Sides A and B are of lengths $2$ and $9$ , respectively, and the angle between A and B is $(3pi)/4$ . What is the length of side C?

Question

1367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-10T10:42:36

$C=10.51$

Since, by the Carnot theorem:

$C^2=A^2+B^2-2ABcos hat (AB)$

in this case

$C=sqrt(2^2+9^2-2*2*9*cos3pi/4$

$C=sqrt(4+81-36*(-sqrt(2)/2))$

$C=sqrt(85+18sqrt(2))$

$C=10.51$

A triangle has sides A, B, and C. Sides A and B are of lengths 22 and 99, respectively, and the angle between A and B is (3pi)/4 (3pi)/4 . What is the length of side C?