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Jonahb · Answer 1 · 2023-07-26T03:20:36+0000

The Law of Cosines is:

$c^2=a^2+b^2-2ab\cdot\cos C$

Where "a", "b" and "c" are sides of the triangle and "C" is the angle opposite side "c".

In this case you know that:

$\begin{gathered} m\angle C=50\degree \\ b=11\operatorname{cm} \\ a=23\operatorname{cm} \\ c=x \end{gathered}$

Then, you can substitute values as following:

$\begin{gathered} c^2=a^2+b^2-2ab\cdot\cos C \\ x^2=(23\operatorname{cm})^2+(11\operatorname{cm})^2-2(23\operatorname{cm})(11\operatorname{cm})\cdot\cos (50\degree) \end{gathered}$

Finally, evaluating, you get that the answer is:

$\begin{gathered} \\ x\approx18.02\operatorname{cm} \end{gathered}$

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