Question

39. Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a

cable. If the length of the cables are 72 meters and 77 meters and the tugboats are 35 meters
apart, find the angle formed between the cables.

Answer 1

`26.903^(\circ)`

Explanation:

a = 77 m

b = 72 m

c = Distance between the tugboats = 35 m

`m\angle C` = Angle between the cables

`c^2=a^2+b^2-2ab\cos C\\\Rightarrow m\angle C=\cos^(-1)(c^2-a^2-b^2)/(-2ab)\\\Rightarrow m\angle C=\cos^(-1)(35^2-77^2-72^2)/(-2* 77* 72)\\\Rightarrow m\angle C=26.903^(\circ)`

The angle formed between the cables is
`26.903^(\circ)`.