I think the inclusion of 2 miles as the distance between the boats is an error in the question since it is the distance between the two boats that we were asked to calculate, being given the distances of the boats from the dock and the angle between the two boats. Please also kindly, see the attached for a diagrammatic representation of this scenario
Answer: The distance between the boats is 5.14 miles
Step-by-step explanation:
Extracting key information from the question:
*** The angle between the two boats approaching a dock is 118°
*** The boats are 3 miles from each other.
*** We are required to calculate the distance between the two boats.
To obtain or calculate the distance between the two boats, we may make use of the cosine rule:
c^2 = (a^2 + b^2) - (2ab× cos C°)
Here, a = 3 miles ( distance between boat "b" & the dock)
"b" = 3 miles as well (distance between boat "a" and the dock)
C° = 118° (the distance between the approaching boats)
c miles = unknown variable (distance between boats "A" & "B")
Then, substituting accordingly:
c^2 =[( 3^2) + (3^2)] - (2×3×3× cos 118°)
c^2 = 9 + 9 - (18 cos 118°)
c^2 = 18 - [18 × (-0.4695)]
c^2 = 18 - (-8.451)
c^2 = 18 + 8.451
c^2 = 26.451
c = √26.451
c = 5.14 miles
Therefore, the distance between the two boats is 5.14 miles
