A triangle has sides A, B, and C. Sides A and B are of lengths $8$ $8$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?

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Answer 1 · 2018-07-16T08:04:17

$\sqrt{113 - 28 \cdot \sqrt{2} \cdot (\sqrt{3} - 1)}$ $sqrt(113-28*sqrt(2)*(sqrt(3)-1))$

Using the Theorem of cosines:

$c^{2} = a^{2} + b^{2} - 2 a b cos (γ)$ $c^2=a^2+b^2-2abcos(gamma)$
and that

$cos (5 \cdot \frac{π}{12}) = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$ $cos(5*pi/12)=(sqrt(3)-1)/(2sqrt(2))$
we get

$c = \sqrt{113 - 28 \cdot \sqrt{2} (\sqrt{3} - 1)}$ $c=sqrt(113-28*sqrt(2)(sqrt(3)-1))$

A triangle has sides A, B, and C. Sides A and B are of lengths 88 and 77, respectively, and the angle between A and B is 5π12(5pi)/12 . What is the length of side C?