We can see a triangle with the measure of two sides, and also the measure of the included angle as follows:
• a = 216m
,
• b = 110m
,
• c = ?
,
• Angle C = 83°
1. With this given information, we can find the unknown measure of the side c by using the Law of Cosines as follows:
[tex]c^2=a^2+b^2-2abcosC[/tex]
2. Since the triangle is given as follows:
3. Now, we can substitute each of the corresponding values into the formula, and then we can find the value of c as follows:
[tex]\begin{gathered} c^{2}=a^{2}+b^{2}-2abcosC \\ \\ c^2=(216m)^2+(110m)^2-2(216m)(110m)cos(83^{\circ}) \\ \\ c^=\sqrt{(216m)^2+(110m)^2-2(216m)(110m)cos(83^{\circ})} \\ \\ c=\sqrt{52964.7688014m^2} \\ \\ c\approx230.14075867m \end{gathered}[/tex]
If we round the answer to the nearest tenth of a meter, we have that c = 230.1m.
Therefore, in summary, we have that the length of the tunnel is 230.1m.
