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)
<span>C = 107.39 miles</span>
