First, let us calculate the total distance that each have taken after 2 hours.
Let’s say that:
A = sailboat which sails at 23 mph in a direction 330°
B = sailboat which sails at 34 mph in a direction 190°
Calculating for distances:
dA = 23 mph (2 hours) = 46 miles
dB = 34 mph (2 hours) = 68 miles
Imagining a Cartesian coordinate, the angle θ between the two sailboats is simply the difference:
θ = 330° - 190°
θ = 140°
We know that from the law of cosines:
c^2 = a^2 + b^2 – 2 a*b*cos θ
Therefore the distance between the two after 2 hours, C, is:
C^2 = 46^2 + 68^2 – 2 (46) (68) cos(140)
C = 107.39 miles
Based on the speeds and bearing if the boats, the distance separating the board after 2 hours is 107.4 miles.
The total distance travelled be each boat after 2 hours is calculated thus:
Distance of A = 23 × 2 = 46 miles
Distance of B = 34 × 2 = 68 miles
The bearing of each boat is as follows:
A sails at a speeed of 23 mph in a direction 330°
B sails at a speeed of 34 mph in a direction 190°
The angle θ between the two sailboats is:
θ = 330° - 190°
θ = 140°
Using the cosine rule:
[tex]c^{2} = a^{2} + b^{2} – 2 \times a×b×cos θ[/tex]
Where c is the distance between the two after 2 hours and are and b are there respective distances travelled
[tex]C^{2} = 46^{2} + 68^{2} – 2 × 46 × 68 ×cos 140 \\ [/tex]
C = 107.4 miles
Therefore, distance separating the board after 2 hours is 107.4 miles.
Learn more about distance and bearing at: https://brainly.com/question/24142612
