Question

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.C = 109.3°a = 5.6 kmb = 10.7 km

Answer 1

In order to find the third side of this triangle, let's use the law of the cosines:

c² = a²+b²-2.a.b.cosC

$\begin{gathered} c^2=a^2+b^2-2\cdot a\cdot b\cdot\cos C \\ c^2=(5.6)^2+(10.7)^2-2\cdot5.6\cdot10.7\cdot\cos 109.3 \\ c^{2}=31.36+114.49-39.608 \\ c^{2}=106.242 \\ c=10.307 \end{gathered}$

Answer: c = 10.3 km, rounded to the nearest tenth.