Question

View image below. Round your answer to the nearest tenth of a meter.

Answer 1

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:

`c^2=a^2+b^2-2abcosC`

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:

`\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=√(52964.7688014m^2) \\ \\ c\approx230.14075867m \end{gathered}`

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.