## University Calculus: Early Transcendentals (3rd Edition)

The length of side $c$ is approximately $1.951$
$$a = 2 \hspace{1cm}b=3\hspace{1cm}C=40^\circ$$ - Recall the law of cosines: $$c^2=a^2+b^2-2ab\cos C$$ Therefore, we can calculate the length of side $c$: $$c^2=2^2+3^2-2\times2\times3\times\cos40^\circ$$ - Here there is no exact value of $\cos40^\circ$, so we would take an approximate value from calculator, which I would take $\cos40^\circ\approx0.766$ $$c^2=4+9-12\times0.766$$ $$c^2=13-9.192$$ $$c^2=3.808$$ $$c\approx1.951$$ (because the length of a side of a triangle is positive)