Question

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?

Answer 1

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°.

How can the angle between the paths of the boats be found?

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, d1, 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 A is the angle between the paths of the two boats.

Which gives;

$cos(A) = \frac{361}{972}$

$A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ$

• The angle between their paths to the nearest degree, A ≈ 68°

Learn more about the rule of cosines here:

brainly.com/question/13409288

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