Can I get help on this question

Question

Two fishing boats leave the same dock at the same time. One boat travels at a speed of 15 km/h, and the

other boat travels at a speed of 18 km/h. After 45 min, the boats are 14 km apart. Assuming that both boats

are travelling in straight paths, what is the angle between their paths?

Answer 1

For this example, we can assume there is a triangulation between the point at which the two boats leave and the distance between them. In order to determine the angle between the two boats, we must first have all sides of this triangle be represented in terms of distances. These values will be the distances in which the boats have traveled over the 45 minutes (which is equivalent to 0.75 hours):

Boat A: (15km/hr) * (0.75hr) = 11.25km

Boat B: (18km.hr) * (0.75 hr) = 13.5km

Distance Between Boats = 14 km.

Since this triangle is NOT a right triangle, we have to use the Law of Cosines to find this distance. The Law of Cosines can be modeled by: c² = a² + b² - 2*a*b*Cos(C), where C is the angle opposite the longest side "c". In this formula, c = 14, a = 11..25, and b = 13.5, and our goal is to find the measure of C:

(14)² = (11.25)² + (13.5)² - 2(11.25)(13.5)Cos(C)

196 = 126.5625 + 182.25 - 303.75Cos(C)

-112.8125 = -303.75Cos(C)

Cos(C) = 112.8125/303.75

C = Cos^-1(112.8125/303.75)

C = 68.2^o

Therefore, the approximate angle between the two boats when they leave the same dock is 68.2 degrees.