The Law of the Cosines is used when two sides and the angle between them are known in a given triangle.
Let a and c two known sides of a triangle, and B the angle included, thus, the unknown side b is calculated as:
[tex]b^2=a^2+c^2-2ac\cos B[/tex]
Substituting the given values a = 76 km, c = 88 km, B = 40.8°:
[tex]b^2=76^2+88^2-2(76)(88)\cos40.8\~[/tex]
Calculating:
[tex]\begin{gathered} b^2=3394.4341 \\ \\ b=\sqrt{3394.4341} \\ \\ b=58.26 \end{gathered}[/tex]
Distance between the installations: 58.26 Km
