A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 3 vessels is `5^(@)`. The approximate distance in miles, from the cargo ship to the fishing boat is given by which of the following expressions?
(Note: The law of cosines states that for any triangle with vertices A, B and C adn the sides opposite those vertices with length a, b, and c, respectively. `c^(2) = a^(2) + b^(2) - 2ab cos C`).

Options

A. `sqrt((5.0)^(2) - (4.2)^(2))`
B. `sqrt((4.2)^(2) + (5.0)^(2) - 2 cdot 4.2 cdot 5.0 cos 5^(@))`
C. `sqrt((4.2)^(2) + (5.0)^(2) + 2 cdot 4.2 cdot 5.0 cos 5^(@))`
D. `sqrt((4.2)^(2) + (5.0)^(2) - 2 cdot 4.2 cdot 5.0 cos 85^(@))`

Answer

B