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Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?

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onyebuchinnaji

The angle between their paths to the nearest degree is 68⁰.

Displacement of each boats after 45 minutes

first displacement, a = 15 km/h  x (45/60)

first displacement, a = 11.25 km

second displacement, b = 18 km/h  x (45/60)

                                     b = 13.5 km

Angle between their paths to the nearest degree

c² = a² + b² - 2ab(cosθ)

2ab(cosθ) = a² + b² - c²

cosθ =  (a² + b² - c²)/(2ab)

cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)

cosθ = 0.371

θ = arc cos(0.371)

θ = 68.22 ⁰

Thus, the angle between their paths to the nearest degree is 68⁰.

Learn more about angles here: https://brainly.com/question/25716982

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