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

Answer:

$26.903^{\circ}$

Step-by-step explanation:

a = 77 m

b = 72 m

c = Distance between the tugboats = 35 m

$m\angle C$ = Angle between the cables

$c^2=a^2+b^2-2ab\cos C\\\Rightarrow m\angle C=\cos^{-1}\dfrac{c^2-a^2-b^2}{-2ab}\\\Rightarrow m\angle C=\cos^{-1}\dfrac{35^2-77^2-72^2}{-2\times 77\times 72}\\\Rightarrow m\angle C=26.903^{\circ}$

The angle formed between the cables is $26.903^{\circ}$.