Two ships leave a harbor at the same time. One ship travels on a bearing S 13 degrees W at 16 miles per hour. The other ship tra
vels on a bearing N 75 degrees E at 11 miles per hour. How far apart will the ships be after 2 hours?
1 answer:
Answer:
47 miles
Explanation:
From the diagrammatic representation below;we can observe the illustration of the question.
after two hours;
The first ship = 16 miles per hour × 2 hours = 32 hours
the second ship = 11 miles per hour × 2 hours = 22 hours
to solve for ΔQPR in the diagram; we have;
∠ P = 13° + (2nd quadrant) + 15°
∠ P = 13° + 90° + 15°
∠ P = 118°
To solve for the distance apart the two ship, we can see from the diagram that it is "p". So, using cosine rule; we have:
p² = q² + r² - 2qr Cos P
p² = 22² + 32² - 2(22)(32) Cos 118°
p² = 484 + 1024 - (1408) (-0.4695)
p² = 1508 + 661.056
p² = 2169.056
p =
p = 46.5731252
p ≅ 47 miles
∴ The ships will be 47 miles far apart after 2 hours.
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