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2020-04-06 1:08 pm
Ship A sails at 10mph on a bearing of N30W. Ship B sails at 12mph on a bearing of N30E. If they started from the same point at the same time, how far apart are they after 2 hours?
回答 (1)
2020-04-06 2:07 pm
Refer to the figure below.
O: The starting point of the both ships
A: The position of ship A after 2 hours
B: The position of ship B after 2 hours
OA = (10 miles/hr) × (2 hr) = 20 miles
OB = (12 miles/hr) × (2 hr) = 24 miles
∠AOB = 30° + 30° = 60°
AB² = OA² + OB² + 2 × OA × OB × cos(∠AOB) … (cosine law)
AB² = 20² + 24² + 2 × 20 × 24 × cos(60°) sq. miles
AB = √[20² + 24² + 2 × 20 × 24 × cos(60°)] miles
AB = 22.3 miles
The two ships are 22.3 miles apart.
O: The starting point of the both ships
A: The position of ship A after 2 hours
B: The position of ship B after 2 hours
OA = (10 miles/hr) × (2 hr) = 20 miles
OB = (12 miles/hr) × (2 hr) = 24 miles
∠AOB = 30° + 30° = 60°
AB² = OA² + OB² + 2 × OA × OB × cos(∠AOB) … (cosine law)
AB² = 20² + 24² + 2 × 20 × 24 × cos(60°) sq. miles
AB = √[20² + 24² + 2 × 20 × 24 × cos(60°)] miles
AB = 22.3 miles
The two ships are 22.3 miles apart.
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