Question

Two boats left the harbour at the same time. One travelled at 10km/h on a bearing N47degreeE. The other traveled at 8km/h on a bearing of N79degreeE. How far apart are the boats after 45min? Round the distance to nearest tenth of a km.

Answer 1

4.0 km

Explanation:

You want the distance between two boats after 45 minutes if they left at the same time and traveled 10 km/h at N47E, and 8 km/h at N79E.

Law of cosines

The distances the boats traveled in 3/4 hour can be found by multiplying the speed by the time:

distance = speed · time

distance = {10 km/h, 8 km/h} · (3/4 h) = {7.5 km, 6 km}

The distance between their positions can be found from the law of cosines:

c² = a² +b² -2ab·cos(C)

Here, the angle between the vectors is 79° -47° = 32°, so the distance is given by ...

c² = 7.5² +6² -2·7.5·6·cos(32°) ≈ 15.925671

c ≈ √15.925671 ≈ 3.9907

To the nearest tenth km, the distance between the boats is 4.0 km.

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Additional comment

It can be helpful to draw a diagram. A geometry app can measure the distance for you (attachment 1), or a calculator app can calculate it based on the speed vectors (attachment 2).