Answer:
77.3 miles apart (nearest tenth)
Explanation:
Given information:
- Boat A travels north at a speed of 20 mph and a bearing of N32°E.
- Boat B travels at a speed of 28 mph and a bearing of S42°E.
- After 2 hours, Boat A will have travelled 40 miles.
- After 2 hours, Boat B will have travelled 56 miles.
Draw a diagram using the given information (see attached).
To find how far apart the boats are, model as a triangle and find the length of the missing side by using the cosine rule.
From inspection of the drawn diagram:
- a = 40 miles
- b = 56 miles
- c = distance between the boats
- C = 180° - 32° - 42° = 106°
Substitute the values into the cosine rule and solve for c:
Therefore, the boats are 77.3 miles apart (nearest tenth) after 2 hours.