Two boats are approaching a dock. The angle between the two boats is measured as 118 degrees. If the boats are 2 miles from eacg other, nad three miles fron the dock, how far are they from each otjer

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

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

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180