A triangle has sides A, B, and C. Sides A and B are of lengths $6$ and $1$ , respectively, and the angle between A and B is $(7pi)/8$ . What is the length of side C?

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Answer 1 · 2016-02-08T11:00:58

$C ~~ 6.93$

Let the angle opposite to side $A$ be $alpha$ , the angle opposite to side $B$ be $beta$ and the angle opposite to side $C$ be $gamma$ .

Then the law of cosines states:

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

$= 6^2 + 1^2 - 2*6*1cos((7pi)/8)$

$= 37 - 12cos((7pi)/8)$

$~~ 37 - 12 * (-0.92)$

$~~ 48.09 " units"^2$

Thus,

$C ~~ 6.93 " units"$

A triangle has sides A, B, and C. Sides A and B are of lengths 66 and 11, respectively, and the angle between A and B is (7pi)/8 (7pi)/8 . What is the length of side C?