A triangle has sides A, B, and C. Sides A and B are of lengths $1$ and $3$ , respectively, and the angle between A and B is $(5pi)/6$ . What is the length of side C?

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Answer 1 · 2018-03-29T10:30:37

c=3.66

$cos(C)=(a^2+b^2-c^2)/(2ab)$
or
$c=sqrt(a^2+b^2-2abcos(C))$

We know that the sides a and b are 1 and 3
We know the angle between them Angle C is $(5pi)/6$

$c=sqrt((1)^2+(3)^2-2(1)(3)cos((5pi)/6))$

$c=sqrt((1+9-6(sqrt3/2)$

$c=sqrt((10-3sqrt3/2)$

Enter into a calculator

$c=3.66$

A triangle has sides A, B, and C. Sides A and B are of lengths 11 and 33, respectively, and the angle between A and B is (5pi)/6 (5pi)/6 . What is the length of side C?