The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.
<h3>How can the angle between the paths of the boats be found?</h3>
The given parameters are;
Direction of the first boat = Northeast
Speed of the first boat = 15 km/h
Direction of the second boat = Northwest
Speed of the second boat = 18 km/h
Distance between the boats after 45 minutes = 14.0 km.
45 minutes = 0.75 × 1 hour
Distance traveled by the first boat in 45 minutes, <em>d1</em>,<em> </em>is therefore;
d1 = 15 km/h × 0.75 hr = 11.25 km
For the second boat, we have;
d2 = 18 km/h × 0.75 hr = 13.5 km
Using cosine rule, we have;
14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)
Where <em>A </em>is the angle between the paths of the two boats.
Which gives;
- The angle between their paths to the nearest degree, <em>A</em><em> </em>≈ 68°
Learn more about the rule of cosines here:
brainly.com/question/13409288
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